C3test_3_instanton.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    164587,       4582]
NotebookOptionsPosition[    159230,       4491]
NotebookOutlinePosition[    159595,       4507]
CellTagsIndexPosition[    159552,       4504]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[{
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "+", "1"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", "z", "]"}], 
   RowBox[{"G", "[", "z", "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "+", "2"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "1"}], "]"}], 
   RowBox[{"G", "[", 
    RowBox[{"z", "+", "1"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "+", "3"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "2"}], "]"}], 
   RowBox[{"G", "[", 
    RowBox[{"z", "+", "2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "+", "4"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "3"}], "]"}], 
   RowBox[{"G", "[", 
    RowBox[{"z", "+", "3"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "-", "1"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"G", "[", "z", "]"}], "/", 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "1"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "-", "2"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"G", "[", 
    RowBox[{"z", "-", "1"}], "]"}], "/", 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "-", "3"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"G", "[", 
    RowBox[{"z", "-", "2"}], "]"}], "/", 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "3"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"z_", "-", "4"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"G", "[", 
    RowBox[{"z", "-", "3"}], "]"}], "/", 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "4"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"w_", " ", 
    RowBox[{"(", 
     RowBox[{"z_", " ", "+", " ", "y_"}], ")"}]}], "]"}], ":=", 
  RowBox[{"G", "[", 
   RowBox[{
    RowBox[{"w", " ", "z"}], " ", "+", " ", 
    RowBox[{"w", " ", "y"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{
    RowBox[{"w_", " ", 
     RowBox[{"(", 
      RowBox[{"z_", " ", "+", " ", "y_"}], ")"}]}], "+", "x_"}], "]"}], ":=", 
  
  RowBox[{"G", "[", 
   RowBox[{
    RowBox[{"w", " ", "z"}], " ", "+", " ", 
    RowBox[{"w", " ", "y"}], "+", "x"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "+", "1"}], "]"}], ":=", 
  RowBox[{"z", " ", 
   RowBox[{"\[CapitalGamma]", "[", "z", "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "+", "2"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"z", "+", "1"}], ")"}], 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "1"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "+", "3"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"z", "+", "2"}], ")"}], 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "+", "4"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"z", "+", "3"}], ")"}], 
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "+", "3"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "-", "1"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", "z", "]"}], "/", 
   RowBox[{"(", 
    RowBox[{"z", "-", "1"}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "-", "2"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "1"}], "]"}], "/", 
   RowBox[{"(", 
    RowBox[{"z", "-", "2"}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "-", "3"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "2"}], "]"}], "/", 
   RowBox[{"(", 
    RowBox[{"z", "-", "3"}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"z_", "-", "4"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"\[CapitalGamma]", "[", 
    RowBox[{"z", "-", "3"}], "]"}], "/", 
   RowBox[{"(", 
    RowBox[{"z", "-", "4"}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{"w_", " ", 
    RowBox[{"(", 
     RowBox[{"z_", " ", "+", " ", "y_"}], ")"}]}], "]"}], ":=", 
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{
    RowBox[{"w", " ", "z"}], " ", "+", " ", 
    RowBox[{"w", " ", "y"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{
    RowBox[{"w_", " ", 
     RowBox[{"(", 
      RowBox[{"z_", " ", "+", " ", "y_"}], ")"}]}], "+", "x_"}], "]"}], ":=", 
  
  RowBox[{"\[CapitalGamma]", "[", 
   RowBox[{
    RowBox[{"w", " ", "z"}], " ", "+", " ", 
    RowBox[{"w", " ", "y"}], "+", "x"}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.8000190448143587`*^9, 3.80001912608195*^9}, 
   3.80154421701086*^9},
 FontSize->9,
 CellLabel->"In[1]:=",ExpressionUUID->"7fbbfe53-669a-4751-a8c1-45b12bcf4019"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"D3RootList", " ", "=", " ", 
   RowBox[{"Flatten", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"If", "[", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            RowBox[{"a", "^", "2"}], "+", 
            RowBox[{"b", "^", "2"}], "+", 
            RowBox[{"c", "^", "2"}]}], "\[Equal]", "2"}], ")"}], ",", 
         RowBox[{"{", 
          RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", "Nothing"}], "]"}], 
       ",", 
       RowBox[{"{", 
        RowBox[{"a", ",", 
         RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"b", ",", 
         RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"c", ",", 
         RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}], ",", "2"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"C3RootList", " ", "=", " ", 
   RowBox[{"Join", "[", 
    RowBox[{"D3RootList", ",", 
     RowBox[{"Flatten", "[", 
      RowBox[{
       RowBox[{"2", 
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{"If", "[", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{"a", "^", "2"}], "+", 
               RowBox[{"b", "^", "2"}], "+", 
               RowBox[{"c", "^", "2"}]}], "\[Equal]", "1"}], ")"}], ",", 
            RowBox[{"{", 
             RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", "Nothing"}], 
           "]"}], ",", 
          RowBox[{"{", 
           RowBox[{"a", ",", 
            RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"b", ",", 
            RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"c", ",", 
            RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}]}], ",", "2"}], 
      "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   SubscriptBox["G", "0"], "[", 
   RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_", ",", "\[Sigma]3_"}], "]"}], ":=", 
  
  RowBox[{
   RowBox[{"1", "/", 
    RowBox[{"Product", "[", 
     RowBox[{
      RowBox[{"Abs", "[", 
       RowBox[{"G", "[", 
        RowBox[{"1", "+", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3"}], "}"}], 
          ".", "a"}]}], "]"}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"a", ",", "C3RootList"}], "}"}]}], "]"}]}], "//.", 
   RowBox[{
    RowBox[{"Abs", "[", 
     RowBox[{"x_", " ", "y_"}], " ", "]"}], "\[Rule]", " ", 
    RowBox[{
     RowBox[{"Abs", "[", "x", "]"}], 
     RowBox[{"Abs", "[", "y", "]"}]}]}]}]}]}], "Input",
 CellChangeTimes->{{3.801366960878847*^9, 3.801366972457995*^9}, {
  3.8013670333244963`*^9, 3.801367037103655*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"13ba7768-eb8f-4690-9f95-b9283709dfb4"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"2", "\[Sigma]2"}], ")"}], "2"], 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"2", " ", "\[Sigma]3"}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"\[Sigma]2", "+", "\[Sigma]3"}], ")"}], "2"], 
      RowBox[{
       SubscriptBox["G", "0"], "[", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], "+", "\[Sigma]2"}], ",", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], "+", "\[Sigma]3"}]}], "]"}], " ", 
      RowBox[{
       SubscriptBox["G", "0"], "[", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
        RowBox[{
         FractionBox["1", "2"], "+", "\[Sigma]2"}], ",", 
        RowBox[{
         FractionBox["1", "2"], "+", "\[Sigma]3"}]}], "]"}]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "-", 
         RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
      RowBox[{
       SubscriptBox["G", "0"], "[", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2", ",", 
        "\[Sigma]3"}], "]"}], " ", 
      RowBox[{
       SubscriptBox["G", "0"], "[", 
       RowBox[{"\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3"}], "]"}]}], 
     ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Sigma]1", " ", ">", "0"}], ",", " ", 
     RowBox[{"\[Sigma]2", " ", ">", "0"}], ",", 
     RowBox[{"\[Sigma]3", ">", "0"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.801367090894209*^9, 3.801367158507928*^9}, {
  3.801368139717504*^9, 3.801368171939479*^9}, {3.8013753066535387`*^9, 
  3.801375319794949*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"33ccae59-5abe-41fa-8607-c77230430fb8"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{{3.8013671377041063`*^9, 3.80136715960043*^9}, {
  3.801368153480854*^9, 3.8013681727825603`*^9}, {3.801544221689867*^9, 
  3.80154422629595*^9}},
 CellLabel->"Out[25]=",ExpressionUUID->"89e495a0-01a9-4c0c-9f80-8ec3c2549d50"]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"A", "[", 
    RowBox[{
    "i_", ",", "l1_", ",", "l2_", ",", "l3_", ",", "s1_", ",", "s2_", ",", 
     "s3_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"\[Epsilon]1", "^", 
     RowBox[{"(", 
      RowBox[{"l1", "+", "s1"}], ")"}]}], 
    RowBox[{"\[Epsilon]2", "^", 
     RowBox[{"(", 
      RowBox[{"l2", "+", "s2"}], ")"}]}], 
    SuperscriptBox["\[Epsilon]3", 
     RowBox[{"l3", "+", "s2"}]], 
    RowBox[{"\[Xi]", "^", 
     RowBox[{"(", 
      RowBox[{"i", "+", 
       FractionBox[
        RowBox[{
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l1", "+", "s1"}], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l2", "+", "s2"}], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l3", "+", "s3"}], ")"}], "2"]}], 
        RowBox[{"2", " "}]]}], ")"}]}], 
    RowBox[{"t", "^", 
     RowBox[{"(", 
      RowBox[{"i", "+", 
       FractionBox[
        RowBox[{
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l1", "+", "\[Sigma]1", "+", "s1"}], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l2", "+", "\[Sigma]2", "+", "s2"}], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"l3", "+", "\[Sigma]3", "+", "s3"}], ")"}], "2"]}], 
        RowBox[{"2", " "}]]}], ")"}]}], 
    RowBox[{"F0", "[", 
     RowBox[{
      RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
      RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
      RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}], 
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{"i", "\[Equal]", "0"}], ",", "1", ",", 
      RowBox[{
       SubscriptBox["Z", "i"], "[", 
       RowBox[{
        RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
        RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
        RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}]}], "]"}], 
    RowBox[{"E", "^", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"\[Eta]1", 
        RowBox[{"(", 
         RowBox[{"l1", "+", "s1"}], ")"}]}], "+", 
       RowBox[{"\[Eta]2", " ", 
        RowBox[{"(", 
         RowBox[{"l2", "+", "s2"}], ")"}]}], "+", 
       RowBox[{"\[Eta]3", 
        RowBox[{"(", 
         RowBox[{"l3", "+", "s3"}], ")"}]}]}], ")"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"e", "[", 
    RowBox[{
    "i_", ",", "l1_", ",", "l2_", ",", "l3_", ",", "s1_", ",", "s2_", ",", 
     "s3_"}], "]"}], ":=", 
   RowBox[{"i", "+", 
    FractionBox[
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"l1", "+", "\[Sigma]1", "+", "s1"}], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"l2", "+", "\[Sigma]2", "+", "s2"}], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"l3", "+", "\[Sigma]3", "+", "s3"}], ")"}], "2"]}], 
     RowBox[{"2", " "}]]}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.801373727636726*^9, 3.801373785831159*^9}, {
   3.801374192044167*^9, 3.801374201897221*^9}, {3.801374604153385*^9, 
   3.801374673144751*^9}, 3.801375179002427*^9},
 CellLabel->"In[26]:=",ExpressionUUID->"cbf7f7ef-2308-4799-a4df-dc52a26115cb"],

Cell[BoxData[
 RowBox[{"(*", "LHS", "*)"}]], "Input",
 CellChangeTimes->{{3.801375144335328*^9, 
  3.8013751465213547`*^9}},ExpressionUUID->"69b8ce18-ed8a-4a71-ac1a-\
926da1fb788d"],

Cell[BoxData[
 RowBox[{"Total", "[", 
  RowBox[{
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"Coefficient", "[", 
      RowBox[{
       RowBox[{"Coefficient", "[", 
        RowBox[{
         RowBox[{"Coefficient", "[", 
          RowBox[{
           RowBox[{
           "Coefficient", "[", "  ", "\[IndentingNewLine]", 
            "\[IndentingNewLine]", 
            RowBox[{
             RowBox[{
              RowBox[{"A", "[", 
               RowBox[{
               "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "+", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              "\[IndentingNewLine]", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "+", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}]}], 
             "\[IndentingNewLine]", "\[IndentingNewLine]", ",", "\[Xi]", ",", 
             
             RowBox[{"1", "/", "2"}]}], "]"}], ",", "\[Epsilon]1", ",", "1"}],
           "]"}], ",", "\[Epsilon]2", ",", "0"}], "]"}], ",", "\[Epsilon]3", 
       ",", "0"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"i1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p", ",", "0", ",", "1", ",", 
       RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}], "//", "Flatten"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.80137470434205*^9, 3.801374977036191*^9}, {
  3.8013750396927567`*^9, 
  3.8013751392246723`*^9}},ExpressionUUID->"7886a0f0-8552-4412-8237-\
ebbaff04e0a2"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Total", "[", 
   RowBox[{
    RowBox[{"Table", "[", "  ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"A", "[", 
         RowBox[{
         "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "+", 
           RowBox[{"e", "[", 
            RowBox[{
            "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "+", 
           RowBox[{"e", "[", 
            RowBox[{
            "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}]}], "\[IndentingNewLine]", 
       "\[IndentingNewLine]", "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"i", "\[Rule]", "0"}], ",", 
         RowBox[{"j", "\[Rule]", "0"}], ",", 
         RowBox[{"k", "\[Rule]", "0"}], ",", 
         RowBox[{"l", "\[Rule]", "0"}], ",", 
         RowBox[{"m", "\[Rule]", "0"}], ",", 
         RowBox[{"n", "\[Rule]", "0"}], ",", 
         RowBox[{"o", "\[Rule]", "0"}], ",", 
         RowBox[{"p", "\[Rule]", "1"}], ",", 
         RowBox[{"i1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"i2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"i3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"j1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}], ",", 
         RowBox[{"j2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "5", "]"}], "]"}]}], ",", 
         RowBox[{"j3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "6", "]"}], "]"}]}], ",", 
         RowBox[{"k1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "7", "]"}], "]"}]}], ",", 
         RowBox[{"k2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "8", "]"}], "]"}]}], ",", 
         RowBox[{"k3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "9", "]"}], "]"}]}], ",", 
         RowBox[{"l1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "10", "]"}], "]"}]}], ",", 
         RowBox[{"l2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "11", "]"}], "]"}]}], ",", 
         RowBox[{"l3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "12", "]"}], "]"}]}], ",", 
         RowBox[{"m1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "13", "]"}], "]"}]}], ",", 
         RowBox[{"m2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "14", "]"}], "]"}]}], ",", 
         RowBox[{"m3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "15", "]"}], "]"}]}], ",", 
         RowBox[{"n1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "16", "]"}], "]"}]}], ",", 
         RowBox[{"n2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "17", "]"}], "]"}]}], ",", 
         RowBox[{"n3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "18", "]"}], "]"}]}], ",", 
         RowBox[{"o1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "19", "]"}], "]"}]}], ",", 
         RowBox[{"o2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "20", "]"}], "]"}]}], ",", 
         RowBox[{"o3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "21", "]"}], "]"}]}], ",", 
         RowBox[{"p1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "22", "]"}], "]"}]}], ",", 
         RowBox[{"p2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "23", "]"}], "]"}]}], ",", 
         RowBox[{"p3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "24", "]"}], "]"}]}]}], "}"}]}], 
      "\[IndentingNewLine]", ",", 
      RowBox[{"{", 
       RowBox[{"a", ",", 
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"1", "/", "2"}], 
           RowBox[{"UnitVector", "[", 
            RowBox[{"24", ",", "i"}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"i", ",", "1", ",", "24"}], "}"}]}], "]"}]}], "}"}]}], 
     "]"}], "//", "Flatten"}], "]"}], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.801375233463986*^9, 3.801375241971634*^9}, {
  3.80154428262195*^9, 3.801544391713751*^9}, {3.801544986640678*^9, 
  3.80154514541999*^9}, {3.8015462587148743`*^9, 3.80154625928255*^9}},
 CellLabel->"In[32]:=",ExpressionUUID->"2ff49383-25ea-4cad-bf7e-4594c863785b"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{
  3.8015450980107317`*^9, {3.8015451309397783`*^9, 3.801545145934346*^9}, 
   3.801546259950736*^9},
 CellLabel->"Out[32]=",ExpressionUUID->"27a4126f-4994-46ed-9363-b23e5e86955d"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"Total", "[", 
   RowBox[{
    RowBox[{"Table", "[", "  ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"A", "[", 
         RowBox[{
         "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{"A", "[", 
         RowBox[{
         "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", "0"}],
          "]"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "+", 
           RowBox[{"e", "[", 
            RowBox[{
            "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"e", "[", 
            RowBox[{
            "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "+", 
           RowBox[{"e", "[", 
            RowBox[{
            "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
             "0"}], "]"}], "-", 
           RowBox[{"e", "[", 
            RowBox[{
            "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
             "0"}], "]"}]}], ")"}], "^", "2"}]}], "\[IndentingNewLine]", 
       "\[IndentingNewLine]", "/.", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"i", "\[Rule]", "0"}], ",", 
         RowBox[{"j", "\[Rule]", "0"}], ",", 
         RowBox[{"k", "\[Rule]", "0"}], ",", 
         RowBox[{"l", "\[Rule]", "0"}], ",", 
         RowBox[{"m", "\[Rule]", "0"}], ",", 
         RowBox[{"n", "\[Rule]", "0"}], ",", 
         RowBox[{"o", "\[Rule]", "0"}], ",", 
         RowBox[{"p", "\[Rule]", "1"}], ",", 
         RowBox[{"i1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"i2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"i3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"j1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}], ",", 
         RowBox[{"j2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "5", "]"}], "]"}]}], ",", 
         RowBox[{"j3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "6", "]"}], "]"}]}], ",", 
         RowBox[{"k1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "7", "]"}], "]"}]}], ",", 
         RowBox[{"k2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "8", "]"}], "]"}]}], ",", 
         RowBox[{"k3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "9", "]"}], "]"}]}], ",", 
         RowBox[{"l1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "10", "]"}], "]"}]}], ",", 
         RowBox[{"l2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "11", "]"}], "]"}]}], ",", 
         RowBox[{"l3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "12", "]"}], "]"}]}], ",", 
         RowBox[{"m1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "13", "]"}], "]"}]}], ",", 
         RowBox[{"m2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "14", "]"}], "]"}]}], ",", 
         RowBox[{"m3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "15", "]"}], "]"}]}], ",", 
         RowBox[{"n1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "16", "]"}], "]"}]}], ",", 
         RowBox[{"n2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "17", "]"}], "]"}]}], ",", 
         RowBox[{"n3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "18", "]"}], "]"}]}], ",", 
         RowBox[{"o1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "19", "]"}], "]"}]}], ",", 
         RowBox[{"o2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "20", "]"}], "]"}]}], ",", 
         RowBox[{"o3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "21", "]"}], "]"}]}], ",", 
         RowBox[{"p1", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "22", "]"}], "]"}]}], ",", 
         RowBox[{"p2", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "23", "]"}], "]"}]}], ",", 
         RowBox[{"p3", "\[Rule]", " ", 
          RowBox[{"a", "[", 
           RowBox[{"[", "24", "]"}], "]"}]}]}], "}"}]}], 
      "\[IndentingNewLine]", ",", 
      RowBox[{"{", 
       RowBox[{"a", ",", 
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"1", "/", "2"}], 
           RowBox[{"UnitVector", "[", 
            RowBox[{"24", ",", "i"}], "]"}]}], ",", 
          RowBox[{"{", 
           RowBox[{"i", ",", "1", ",", "24"}], "}"}]}], "]"}]}], "}"}]}], 
     "]"}], "//", "Flatten"}], "]"}], "//", "Simplify"}]], "Input",ExpressionU\
UID->"2f73a5d0-6189-4400-a3fc-d8144dfe2a7d"],

Cell[BoxData[
 RowBox[{"Total", "[", 
  RowBox[{
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"Coefficient", "[", 
      RowBox[{
       RowBox[{"Coefficient", "[", 
        RowBox[{
         RowBox[{"Coefficient", "[", 
          RowBox[{
           RowBox[{
           "Coefficient", "[", "  ", "\[IndentingNewLine]", 
            "\[IndentingNewLine]", 
            RowBox[{
             RowBox[{
              RowBox[{"A", "[", 
               RowBox[{
               "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{"A", "[", 
               RowBox[{
               "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", ",", 
                "0"}], "]"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "i", ",", "i1", ",", "i2", ",", "i3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "+", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "j", ",", "j1", ",", "j2", ",", "j3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "k", ",", "k1", ",", "k2", ",", "k3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "l", ",", "l1", ",", "l2", ",", "l3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              "\[IndentingNewLine]", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}], 
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"e", "[", 
                  RowBox[{
                  "m", ",", "m1", ",", "m2", ",", "m3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "+", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "n", ",", "n1", ",", "n2", ",", "n3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "o", ",", "o1", ",", "o2", ",", "o3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}], "-", 
                 RowBox[{"e", "[", 
                  RowBox[{
                  "p", ",", "p1", ",", "p2", ",", "p3", ",", "0", ",", "0", 
                   ",", "0"}], "]"}]}], ")"}], "^", "2"}]}], 
             "\[IndentingNewLine]", "\[IndentingNewLine]", ",", "\[Xi]", ",", 
             
             RowBox[{"1", "/", "2"}]}], "]"}], ",", "\[Epsilon]1", ",", "1"}],
           "]"}], ",", "\[Epsilon]2", ",", "0"}], "]"}], ",", "\[Epsilon]3", 
       ",", "0"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"i1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"l", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"o", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p1", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p3", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p", ",", "0", ",", 
       RowBox[{"1", "/", "2"}], ",", 
       RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}], "//", "Flatten"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.8013752652217903`*^9, 3.801375285842833*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"32e8d142-a8ce-41f0-8b8b-3291527c7e12"],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.801375295267935*^9, 
  3.80137529555219*^9}},ExpressionUUID->"ff50421e-fde3-4253-863c-\
6965bed59fe0"],

Cell[BoxData[
 RowBox[{
  RowBox[{"TauC3", "[", 
   RowBox[{
   "\[Sigma]1_", ",", "\[Sigma]2_", ",", "\[Sigma]3_", ",", "\[Eta]1_", ",", 
    "\[Eta]2_", ",", "\[Eta]3_", ",", "s1_", ",", "s2_", ",", "s3_", ",", 
    "t_"}], "]"}], ":=", 
  RowBox[{"Sum", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Epsilon]1", "^", 
      RowBox[{"(", 
       RowBox[{"l1", "+", "s1"}], ")"}]}], 
     RowBox[{"\[Epsilon]2", "^", 
      RowBox[{"(", 
       RowBox[{"l2", "+", "s2"}], ")"}]}], 
     SuperscriptBox["\[Epsilon]3", 
      RowBox[{"l3", "+", "s2"}]], 
     RowBox[{"\[Xi]", "^", 
      RowBox[{"(", 
       RowBox[{"i1", "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l1", "+", "s1"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l2", "+", "s2"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l3", "+", "s3"}], ")"}], "2"]}], 
         RowBox[{"2", " "}]]}], ")"}]}], 
     RowBox[{"t", "^", 
      RowBox[{"(", 
       RowBox[{"i1", "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l1", "+", "\[Sigma]1", "+", "s1"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l2", "+", "\[Sigma]2", "+", "s2"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l3", "+", "\[Sigma]3", "+", "s3"}], ")"}], "2"]}], 
         RowBox[{"2", " "}]]}], ")"}]}], 
     RowBox[{"F0", "[", 
      RowBox[{
       RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
       RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
       RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}], 
     RowBox[{"If", "[", 
      RowBox[{
       RowBox[{"i1", "\[Equal]", "0"}], ",", "1", ",", 
       RowBox[{
        SubscriptBox["Z", "i1"], "[", 
        RowBox[{
         RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
         RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
         RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}]}], "]"}], 
     RowBox[{"E", "^", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Eta]1", 
         RowBox[{"(", 
          RowBox[{"l1", "+", "s1"}], ")"}]}], "+", 
        RowBox[{"\[Eta]2", " ", 
         RowBox[{"(", 
          RowBox[{"l2", "+", "s2"}], ")"}]}], "+", 
        RowBox[{"\[Eta]3", 
         RowBox[{"(", 
          RowBox[{"l3", "+", "s3"}], ")"}]}]}], ")"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"l1", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l2", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l3", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"i1", ",", "0", ",", "1", ",", 
      RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}]}]], "Input",
 InitializationCell->True,
 CellChangeTimes->{{3.7999135617042313`*^9, 3.799913581445242*^9}, {
  3.7999199018498383`*^9, 3.799919914269693*^9}, {3.8000106133370237`*^9, 
  3.8000106197497263`*^9}, {3.801364117321679*^9, 3.8013642372731237`*^9}, {
  3.8013653342066402`*^9, 3.801365342479422*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"a8599c4e-acff-44f7-956a-bde13bbd1df1"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Tau2C3", "[", 
   RowBox[{
   "\[Sigma]1_", ",", "\[Sigma]2_", ",", "\[Sigma]3_", ",", "\[Eta]1_", ",", 
    "\[Eta]2_", ",", "\[Eta]3_", ",", "s1_", ",", "s2_", ",", "s3_", ",", 
    "t_"}], "]"}], ":=", 
  RowBox[{"Sum", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Epsilon]1", "^", 
      RowBox[{"(", 
       RowBox[{"l1", "+", "s1"}], ")"}]}], 
     RowBox[{"\[Epsilon]2", "^", 
      RowBox[{"(", 
       RowBox[{"l2", "+", "s2"}], ")"}]}], 
     SuperscriptBox["\[Epsilon]3", 
      RowBox[{"l3", "+", "s2"}]], 
     RowBox[{"\[Xi]", "^", 
      RowBox[{"(", 
       RowBox[{"i1", "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l1", "+", "s1"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l2", "+", "s2"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l3", "+", "s3"}], ")"}], "2"]}], 
         RowBox[{"2", " "}]]}], ")"}]}], 
     RowBox[{"t", "^", 
      RowBox[{"(", 
       RowBox[{"i1", "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l1", "+", "\[Sigma]1", "+", "s1"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l2", "+", "\[Sigma]2", "+", "s2"}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"l3", "+", "\[Sigma]3", "+", "s3"}], ")"}], "2"]}], 
         RowBox[{"2", " "}]]}], ")"}]}], 
     RowBox[{"F0", "[", 
      RowBox[{
       RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
       RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
       RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}], 
     RowBox[{"If", "[", 
      RowBox[{
       RowBox[{"i1", "\[Equal]", "0"}], ",", "1", ",", 
       RowBox[{
        SubscriptBox["Z", "i1"], "[", 
        RowBox[{
         RowBox[{"\[Sigma]1", "+", "l1", "+", "s1"}], ",", 
         RowBox[{"\[Sigma]2", "+", "l2", "+", "s2"}], ",", 
         RowBox[{"\[Sigma]3", "+", "l3", "+", "s3"}]}], "]"}]}], "]"}], 
     RowBox[{"E", "^", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Eta]1", 
         RowBox[{"(", 
          RowBox[{"l1", "+", "s1"}], ")"}]}], "+", 
        RowBox[{"\[Eta]2", " ", 
         RowBox[{"(", 
          RowBox[{"l2", "+", "s2"}], ")"}]}], "+", 
        RowBox[{"\[Eta]3", 
         RowBox[{"(", 
          RowBox[{"l3", "+", "s3"}], ")"}]}]}], ")"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"l1", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l2", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l3", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"i1", ",", "0", ",", "1", ",", 
      RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.801367967437236*^9, 
  3.801367986214469*^9}},ExpressionUUID->"802de681-664f-4d0f-980f-\
7425f7151347"],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"A", " ", "proposal"}], ",", " ", 
   RowBox[{
    RowBox[{"notice", " ", "the", " ", "half"}], "-", 
    RowBox[{"powers", " ", "of", " ", 
     RowBox[{"instantons", "!"}], " ", "This", " ", "is", " ", "in", " ", 
     "terms", " ", "of", " ", 
     RowBox[{"B2", "."}]}]}]}], "*)"}]], "Input",
 CellChangeTimes->{{3.800010896251151*^9, 
  3.8000109610689077`*^9}},ExpressionUUID->"bcbb43e4-508a-4b68-89ed-\
b456116017b1"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"Coefficient", "[", 
           RowBox[{
            RowBox[{"Coefficient", "[", 
             RowBox[{
              RowBox[{"Coefficient", "[", 
               RowBox[{
                RowBox[{"Coefficient", "[", 
                 RowBox[{
                  RowBox[{
                   RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], 
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], 
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{
                    RowBox[{"p", "^", "2"}], " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}]}], "-", 
                    RowBox[{
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{"p", " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}], "^", "2"}]}], 
                    ")"}]}], ",", "\[Epsilon]1", ",", "k"}], "]"}], ",", 
                "\[Epsilon]2", ",", "l"}], "]"}], ",", "\[Epsilon]3", ",", 
              "m"}], "]"}], ",", "\[Xi]", ",", "n"}], "]"}], "//", 
          "Simplify"}], ")"}], "\[Equal]", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{"Coefficient", "[", 
             RowBox[{
              RowBox[{"Coefficient", "[", 
               RowBox[{
                RowBox[{"Coefficient", "[", 
                 RowBox[{
                  RowBox[{"Coefficient", "[", 
                   RowBox[{
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", "0", ",", 
                    "0", ",", "0", ",", "t"}], "]"}], 
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", "0", ",", 
                    "0", ",", "0", ",", "t"}], "]"}], 
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{"\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", 
                    ",", "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", "0", 
                    ",", "0", ",", "0", ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{
                    RowBox[{"p", "^", "2"}], " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}]}], "-", 
                    RowBox[{
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC3", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Sigma]3", ",", 
                    "\[Eta]1", ",", "\[Eta]2", ",", "\[Eta]3", ",", "0", ",", 
                    "0", ",", "0", ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{"p", " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}], "^", "2"}]}], 
                    ")"}]}], ",", "\[Epsilon]1", ",", "k"}], "]"}], ",", 
                  "\[Epsilon]2", ",", "l"}], "]"}], ",", "\[Epsilon]3", ",", 
                "m"}], "]"}], ",", "\[Xi]", ",", "n"}], "]"}], "//", 
            "Simplify"}], ")"}], "//", "Simplify"}], ")"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"k", ",", 
        RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"l", ",", 
        RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"m", ",", 
        RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"n", ",", "0", ",", "1", ",", 
        RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}], "//", "Flatten"}], "//", 
   "DeleteDuplicates"}], "//", 
  RowBox[{"Simplify", "/.", 
   RowBox[{"t", "\[Rule]", "1"}]}]}]], "Input",
 InitializationCell->True,
 CellChangeTimes->{{3.799914469434128*^9, 3.7999145056873837`*^9}, 
   3.799917119631319*^9, {3.799919382677651*^9, 3.7999194058937387`*^9}, {
   3.80136429766068*^9, 3.8013643182247543`*^9}, {3.801364355866823*^9, 
   3.80136441510533*^9}},
 CellLabel->"In[23]:=",ExpressionUUID->"4f5b7f81-b6c1-4e7e-ad7b-caaacf32513c"],

Cell[BoxData["$Aborted"], "Output",
 CellChangeTimes->{3.80000893942103*^9, 3.80136572944928*^9},
 CellLabel->"Out[23]=",ExpressionUUID->"d6f3e6d5-b07e-4620-888b-a7e32473ec5e"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"1", " ", "loop", " ", "works"}], ",", " ", 
   RowBox[{
   "has", " ", "to", " ", "be", " ", "given", " ", "in", " ", "terms", " ", 
    "of", " ", "C2", " ", "roots"}], ",", " ", 
   RowBox[{"which", " ", "are", " ", "B2", " ", 
    RowBox[{"coroots", "."}]}]}], "*)"}]], "Input",
 CellChangeTimes->{{3.800009674794304*^9, 3.800009677564979*^9}, {
  3.800010934678548*^9, 
  3.800010949142516*^9}},ExpressionUUID->"8f201223-6022-4d60-9d7c-\
ee65f3f5b89c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"4", " ", 
       SuperscriptBox["\[Sigma]2", "2"], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], 
      RowBox[{
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"1", "-", 
          RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], 
       " ", 
       RowBox[{"F0", "[", 
        RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}]], "/.", " ", 
     RowBox[{
      RowBox[{"F0", "[", 
       RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", 
      RowBox[{"1", "/", 
       RowBox[{"Abs", "[", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"G", "[", 
           RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", 
            RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", 
            RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", 
            RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", 
            RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}]}], ")"}], 
        "]"}]}]}]}], "//.", 
    RowBox[{
     RowBox[{"Abs", "[", 
      RowBox[{"x_", " ", "y_"}], " ", "]"}], "\[Rule]", " ", 
     RowBox[{
      RowBox[{"Abs", "[", "x", "]"}], 
      RowBox[{"Abs", "[", "y", "]"}]}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Sigma]1", " ", ">", "0"}], ",", " ", 
     RowBox[{"\[Sigma]2", " ", ">", "0"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.800008983622178*^9, 3.800009002020667*^9}, {
  3.8000190253322477`*^9, 3.800019028832921*^9}},
 CellLabel->
  "In[476]:=",ExpressionUUID->"1529a074-4d71-4fee-962f-1a6fa3e302b5"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{
  3.8000090026170883`*^9, 3.80001902987298*^9, {3.80001907777455*^9, 
   3.8000191291049557`*^9}},
 CellLabel->
  "Out[476]=",ExpressionUUID->"f4fb59ed-aae5-44b9-a818-f5a432273fc1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["t", 
      RowBox[{
       FractionBox["1", "2"], "+", 
       SuperscriptBox["\[Sigma]1", "2"], "+", 
       SuperscriptBox["\[Sigma]2", "2"]}]], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"4", " ", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
       RowBox[{"4", " ", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "-", 
       RowBox[{
        SuperscriptBox[
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
        RowBox[{
         SubscriptBox["Z", 
          FractionBox["1", "2"]], "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}]}], ")"}]}], 
    "\[Equal]", "0"}], ",", 
   RowBox[{
    SubscriptBox["Z", 
     FractionBox["1", "2"]], "[", 
    RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.799920798249586*^9, 3.7999208044638767`*^9}},
 CellLabel->
  "In[137]:=",ExpressionUUID->"e6b6797e-fb4f-42c9-a544-a7d78b436a9f"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     SubscriptBox["Z", 
      FractionBox["1", "2"]], "[", 
     RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "\[Rule]", 
    RowBox[{
     FractionBox["1", 
      SuperscriptBox[
       RowBox[{"F0", "[", 
        RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]], 
     RowBox[{"4", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "-", 
        RowBox[{"2", " ", "\[Sigma]1", " ", "\[Sigma]2", " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{"2", " ", "\[Sigma]1", " ", "\[Sigma]2", " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], 
       ")"}]}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.7999208050601254`*^9},
 CellLabel->
  "Out[137]=",ExpressionUUID->"cfcb0b49-acdb-4be3-8d09-34b95f8a15c6"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{"1", " ", "instanton", " ", "term"}], "*)"}]], "Input",
 CellChangeTimes->{{3.800009682428516*^9, 
  3.800009688889125*^9}},ExpressionUUID->"946a178e-81ac-482b-bf35-\
1aa0522c4009"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      FractionBox["1", 
       SuperscriptBox[
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]], "4", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "-", 
        RowBox[{"2", " ", "\[Sigma]1", " ", "\[Sigma]2", " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{"2", " ", "\[Sigma]1", " ", "\[Sigma]2", " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], "/.",
      " ", 
     RowBox[{
      RowBox[{"F0", "[", 
       RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", 
      RowBox[{"1", "/", 
       RowBox[{"Abs", "[", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"G", "[", 
           RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", 
            RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", 
            RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", 
            RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", 
            RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "-", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
          RowBox[{"G", "[", 
           RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}]}], ")"}], 
        "]"}]}]}]}], "//.", 
    RowBox[{
     RowBox[{"Abs", "[", 
      RowBox[{"x_", " ", "y_"}], " ", "]"}], "\[Rule]", " ", 
     RowBox[{
      RowBox[{"Abs", "[", "x", "]"}], 
      RowBox[{"Abs", "[", "y", "]"}]}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Sigma]1", " ", ">", "0"}], ",", " ", 
     RowBox[{"\[Sigma]2", " ", ">", "0"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.799919509162471*^9, 3.799919564620634*^9}, {
   3.799919677333303*^9, 3.799919694419544*^9}, {3.799920132326584*^9, 
   3.7999201370878553`*^9}, 3.799920685449657*^9, 3.799920814720945*^9, {
   3.800008848681336*^9, 3.800008854963482*^9}, {3.800018968862742*^9, 
   3.800018972812018*^9}},
 CellLabel->
  "In[477]:=",ExpressionUUID->"dd30d338-df56-4756-b60d-bfbc791cd396"],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"2", " ", 
   SuperscriptBox["\[Sigma]1", "2"], " ", 
   SuperscriptBox["\[Sigma]2", "2"]}]]], "Output",
 CellChangeTimes->{
  3.799919529109942*^9, 3.799919565334845*^9, {3.799919681804048*^9, 
   3.799919695385446*^9}, 3.79992013886719*^9, 3.799920686248879*^9, 
   3.799920815683436*^9, {3.800008849422728*^9, 3.800008855480092*^9}, 
   3.800009880395955*^9, 3.800018973693428*^9, 3.800019136687059*^9},
 CellLabel->
  "Out[477]=",ExpressionUUID->"00d4c3bf-2069-4123-afe6-e994f3ee4246"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{"2", " ", "instanton", " ", "term"}], "*)"}]], "Input",
 CellChangeTimes->{{3.8000110311605473`*^9, 
  3.800011034788488*^9}},ExpressionUUID->"75eeb948-90e1-4478-8c7d-\
8cdca2ea5520"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox["1", "4"], "  ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "-", 
              RowBox[{"2", " ", "\[Sigma]1"}], "+", 
              RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", 
              RowBox[{"2", " ", "\[Sigma]1"}], "-", 
              RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
         ")"}]}], "+", 
       RowBox[{
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", "1"}], "+", 
              RowBox[{"2", " ", "\[Sigma]1"}], "+", 
              RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", 
              RowBox[{"2", " ", "\[Sigma]1"}], "+", 
              RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}],
        "-", 
       RowBox[{"4", " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"4", " ", 
           SuperscriptBox["\[Sigma]2", "2"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{"4", " ", 
           SuperscriptBox["\[Sigma]1", "2"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
            "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}], 
          "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"F0", "[", 
             RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", "1"], "[", 
            RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}]}], ")"}]}]}], 
      ")"}]}], "\[Equal]", "0"}], ",", 
   RowBox[{
    SubscriptBox["Z", "1"], "[", 
    RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7999195985850763`*^9, 3.79991960409095*^9}, {
   3.799920098898185*^9, 3.799920105260466*^9}, 3.799920513203062*^9, {
   3.7999205917962437`*^9, 3.799920605580077*^9}},
 CellLabel->
  "In[132]:=",ExpressionUUID->"bc14fa6c-3d3e-4134-afbc-1ec3075c4b2e"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     SubscriptBox["Z", "1"], "[", 
     RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "\[Rule]", 
    RowBox[{"-", 
     RowBox[{
      FractionBox["1", 
       SuperscriptBox[
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]], 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"4", " ", 
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1", ",", 
           RowBox[{
            RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1", ",", 
           RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}], "+", 
        RowBox[{"4", " ", 
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}],
          " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}], "-", 
        
        RowBox[{
         FractionBox["1", "4"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            SuperscriptBox[
             RowBox[{"(", 
              RowBox[{"1", "-", 
               RowBox[{"2", " ", "\[Sigma]1"}], "+", 
               RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
            RowBox[{
             SubscriptBox["Z", 
              FractionBox["1", "2"]], "[", 
             RowBox[{
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"(", 
              RowBox[{"1", "+", 
               RowBox[{"2", " ", "\[Sigma]1"}], "-", 
               RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
            RowBox[{
             SubscriptBox["Z", 
              FractionBox["1", "2"]], "[", 
             RowBox[{
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
          ")"}]}], "-", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            RowBox[{"-", 
             FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"F0", "[", 
          RowBox[{
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
           RowBox[{
            FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            SuperscriptBox[
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", "1"}], "+", 
               RowBox[{"2", " ", "\[Sigma]1"}], "+", 
               RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
            RowBox[{
             SubscriptBox["Z", 
              FractionBox["1", "2"]], "[", 
             RowBox[{
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"(", 
              RowBox[{"1", "+", 
               RowBox[{"2", " ", "\[Sigma]1"}], "+", 
               RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
            RowBox[{
             SubscriptBox["Z", 
              FractionBox["1", "2"]], "[", 
             RowBox[{
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], 
          ")"}]}]}], ")"}]}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.7999196046128073`*^9, 3.799920105784855*^9, {3.799920601095419*^9, 
   3.799920606118011*^9}},
 CellLabel->
  "Out[132]=",ExpressionUUID->"33980c37-0ec3-4974-9f89-8fe7ac937c50"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         FractionBox["1", 
          SuperscriptBox[
           RowBox[{"F0", "[", 
            RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]]}], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"4", " ", 
           SuperscriptBox["\[Sigma]2", "2"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{"4", " ", 
           SuperscriptBox["\[Sigma]1", "2"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
            "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}], 
          "-", 
          RowBox[{
           FractionBox["1", "4"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              SuperscriptBox[
               RowBox[{"(", 
                RowBox[{"1", "-", 
                 RowBox[{"2", " ", "\[Sigma]1"}], "+", 
                 RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
              RowBox[{
               SubscriptBox["Z", 
                FractionBox["1", "2"]], "[", 
               RowBox[{
                RowBox[{
                 RowBox[{"-", 
                  FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                RowBox[{
                 FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
             RowBox[{
              SuperscriptBox[
               RowBox[{"(", 
                RowBox[{"1", "+", 
                 RowBox[{"2", " ", "\[Sigma]1"}], "-", 
                 RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
              RowBox[{
               SubscriptBox["Z", 
                FractionBox["1", "2"]], "[", 
               RowBox[{
                RowBox[{
                 FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                RowBox[{
                 RowBox[{"-", 
                  FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
            ")"}]}], "-", 
          RowBox[{
           FractionBox["1", "4"], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"F0", "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              SuperscriptBox[
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"-", "1"}], "+", 
                 RowBox[{"2", " ", "\[Sigma]1"}], "+", 
                 RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
              RowBox[{
               SubscriptBox["Z", 
                FractionBox["1", "2"]], "[", 
               RowBox[{
                RowBox[{
                 RowBox[{"-", 
                  FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                RowBox[{
                 RowBox[{"-", 
                  FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
             RowBox[{
              SuperscriptBox[
               RowBox[{"(", 
                RowBox[{"1", "+", 
                 RowBox[{"2", " ", "\[Sigma]1"}], "+", 
                 RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
              RowBox[{
               SubscriptBox["Z", 
                FractionBox["1", "2"]], "[", 
               RowBox[{
                RowBox[{
                 FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                RowBox[{
                 FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], 
            ")"}]}]}], ")"}]}], "/.", " ", 
       RowBox[{
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", 
        RowBox[{"1", "/", 
         RowBox[{"Abs", "[", 
          RowBox[{
           RowBox[{"G", "[", 
            RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "-", 
             RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "+", 
             RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "-", 
             RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "+", 
             RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "-", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
           RowBox[{"G", "[", 
            RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}]}], 
          "]"}]}]}]}], "/.", 
      RowBox[{
       RowBox[{
        SubscriptBox["Z", 
         RowBox[{"1", "/", "2"}]], "[", 
        RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", " ", 
       FractionBox["1", 
        RowBox[{"2", " ", 
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         SuperscriptBox["\[Sigma]2", "2"]}]]}]}], "//.", 
     RowBox[{
      RowBox[{"Abs", "[", 
       RowBox[{"x_", " ", "y_"}], " ", "]"}], "\[Rule]", " ", 
      RowBox[{
       RowBox[{"Abs", "[", "x", "]"}], 
       RowBox[{"Abs", "[", "y", "]"}]}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Sigma]1", " ", ">", "0"}], ",", " ", 
      RowBox[{"\[Sigma]2", " ", ">", "0"}]}], "}"}]}], "]"}], "//", 
  "Together"}]], "Input",
 CellChangeTimes->{
  3.799920736124487*^9, {3.79992083648671*^9, 3.799920860694944*^9}, {
   3.799921575522435*^9, 3.7999215811869993`*^9}, {3.8000088094081373`*^9, 
   3.8000088123112698`*^9}, {3.800009756255678*^9, 3.800009781817409*^9}, {
   3.800009838202951*^9, 3.80000983946497*^9}, {3.800019148407425*^9, 
   3.8000191759983063`*^9}},
 CellLabel->
  "In[479]:=",ExpressionUUID->"33a9b55e-cc96-47b8-8a78-b9fab64cb29d"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SuperscriptBox["\[Sigma]1", "2"], "-", 
   RowBox[{"8", " ", 
    SuperscriptBox["\[Sigma]1", "4"]}], "+", 
   RowBox[{"16", " ", 
    SuperscriptBox["\[Sigma]1", "6"]}], "+", 
   SuperscriptBox["\[Sigma]2", "2"], "+", 
   RowBox[{"128", " ", 
    SuperscriptBox["\[Sigma]1", "6"], " ", 
    SuperscriptBox["\[Sigma]2", "2"]}], "-", 
   RowBox[{"8", " ", 
    SuperscriptBox["\[Sigma]2", "4"]}], "-", 
   RowBox[{"256", " ", 
    SuperscriptBox["\[Sigma]1", "4"], " ", 
    SuperscriptBox["\[Sigma]2", "4"]}], "+", 
   RowBox[{"16", " ", 
    SuperscriptBox["\[Sigma]2", "6"]}], "+", 
   RowBox[{"128", " ", 
    SuperscriptBox["\[Sigma]1", "2"], " ", 
    SuperscriptBox["\[Sigma]2", "6"]}]}], 
  RowBox[{"4", " ", 
   SuperscriptBox["\[Sigma]1", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"1", "+", 
      RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
   SuperscriptBox["\[Sigma]2", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"1", "+", 
      RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"]}]]], "Output",
 CellChangeTimes->{
  3.7999207388531322`*^9, 3.799920862415804*^9, 3.799921582614942*^9, 
   3.80000881468684*^9, 3.800009787352844*^9, 3.80000984222248*^9, {
   3.800019158270774*^9, 3.800019177250564*^9}},
 CellLabel->
  "Out[479]=",ExpressionUUID->"b5007431-c6c7-441c-868e-85af1934780d"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
  "Instantons", " ", "according", " ", "to", " ", "Marino", " ", "Wyllard"}], 
  "*)"}]], "Input",
 CellChangeTimes->{{3.800010501109088*^9, 
  3.800010507731896*^9}},ExpressionUUID->"df0aed34-95e2-4d53-830e-\
11f7801f2206"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   SubscriptBox["\[CapitalZHacek]", "1"], "[", 
   RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], ":=", " ", 
  FractionBox["1", 
   RowBox[{"2", 
    RowBox[{"(", 
     RowBox[{"-", 
      RowBox[{"\[Sigma]1", "^", "2"}]}], ")"}], 
    RowBox[{"(", 
     RowBox[{"-", 
      RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}]}]]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalZHacek]", "2"], "[", 
    RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], ":=", " ", 
   RowBox[{
    FractionBox["1", 
     RowBox[{"8", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"\[Sigma]1", "^", "2"}], "-", 
         RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"\[Sigma]2", "^", "2"}], "-", 
         RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}]}]], "+", 
    RowBox[{
     FractionBox["1", 
      RowBox[{"8", " ", "8"}]], "   ", 
     FractionBox["1", 
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"\[Sigma]1", "^", "2"}], "-", 
          RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
       RowBox[{"\[Sigma]1", "^", "2"}], " ", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"\[Sigma]1", "^", "2"}], "-", 
          RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}], "^", "2"}]}]]}], "+", 
    RowBox[{
     FractionBox["1", 
      RowBox[{"8", " ", "8"}]], "   ", 
     FractionBox["1", 
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"\[Sigma]2", "^", "2"}], "-", 
          RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
       RowBox[{"\[Sigma]2", "^", "2"}], " ", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"\[Sigma]1", "^", "2"}], "-", 
          RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}], "^", "2"}]}]]}]}]}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   SubscriptBox["\[CapitalZHacek]", "3"], "[", 
   RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], ":=", 
  RowBox[{
   FractionBox["1", 
    RowBox[{"16", 
     RowBox[{"(", 
      RowBox[{"-", 
       RowBox[{"\[Sigma]1", "^", "2"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"-", 
       RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}], " "}]], 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      FractionBox["2", "9"], 
      FractionBox["1", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", "1"}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]2", "^", "2"}], "-", "1"}], ")"}], "^", 
         "2"}]}]]}], "+", 
     RowBox[{
      FractionBox["1", "9"], 
      FractionBox["1", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", 
           RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]2", "^", "2"}], "-", 
           RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}]}]]}], "+", 
     RowBox[{
      FractionBox["1", "8"], "   ", 
      FractionBox[
       RowBox[{"\[Sigma]1", "^", "2"}], 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", 
           RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", "1"}], ")"}], "^", "2"}], 
        " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", 
           RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}], "^", "2"}]}]]}], "+", 
     RowBox[{
      FractionBox["1", "8"], "   ", 
      FractionBox[
       RowBox[{"\[Sigma]2", "^", "2"}], 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]2", "^", "2"}], "-", 
           RowBox[{"1", "/", "4"}]}], ")"}], "^", "2"}], 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]2", "^", "2"}], "-", "1"}], ")"}], "^", "2"}], 
        " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Sigma]1", "^", "2"}], "-", 
           RowBox[{"\[Sigma]2", "^", "2"}]}], ")"}], "^", "2"}]}]]}]}], " ", 
    ")"}], " "}]}]}], "Input",
 InitializationCell->True,
 CellChangeTimes->{{3.7999224297462187`*^9, 3.799922533792199*^9}, {
   3.7999227277538853`*^9, 3.7999227341109667`*^9}, {3.799922878752627*^9, 
   3.7999228816152887`*^9}, {3.799922971968774*^9, 3.799922983146391*^9}, {
   3.799923013492688*^9, 3.799923071858177*^9}, {3.799923548136063*^9, 
   3.7999235505730343`*^9}, {3.800010027571669*^9, 3.8000100296980352`*^9}, {
   3.800010121331751*^9, 3.800010137009275*^9}, {3.800010318228232*^9, 
   3.800010470984029*^9}, 3.800010789212764*^9, {3.800011069045322*^9, 
   3.800011072420987*^9}},
 CellLabel->
  "In[409]:=",ExpressionUUID->"6ab92e69-3298-4e5d-8c38-8c47a9b03d0d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   SubscriptBox["\[CapitalZHacek]", "2"], "[", 
   RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "//", 
  "Together"}]], "Input",
 CellChangeTimes->{{3.8000111429502773`*^9, 3.800011158451153*^9}},
 CellLabel->
  "In[413]:=",ExpressionUUID->"de09ef28-b5cc-4eaf-8c57-76e9a86981bb"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SuperscriptBox["\[Sigma]1", "2"], "-", 
   RowBox[{"8", " ", 
    SuperscriptBox["\[Sigma]1", "4"]}], "+", 
   RowBox[{"16", " ", 
    SuperscriptBox["\[Sigma]1", "6"]}], "+", 
   SuperscriptBox["\[Sigma]2", "2"], "+", 
   RowBox[{"128", " ", 
    SuperscriptBox["\[Sigma]1", "6"], " ", 
    SuperscriptBox["\[Sigma]2", "2"]}], "-", 
   RowBox[{"8", " ", 
    SuperscriptBox["\[Sigma]2", "4"]}], "-", 
   RowBox[{"256", " ", 
    SuperscriptBox["\[Sigma]1", "4"], " ", 
    SuperscriptBox["\[Sigma]2", "4"]}], "+", 
   RowBox[{"16", " ", 
    SuperscriptBox["\[Sigma]2", "6"]}], "+", 
   RowBox[{"128", " ", 
    SuperscriptBox["\[Sigma]1", "2"], " ", 
    SuperscriptBox["\[Sigma]2", "6"]}]}], 
  RowBox[{"4", " ", 
   SuperscriptBox["\[Sigma]1", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"4", " ", 
       SuperscriptBox["\[Sigma]1", "2"]}]}], ")"}], "2"], " ", 
   SuperscriptBox["\[Sigma]2", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["\[Sigma]1", "2"], "-", 
      SuperscriptBox["\[Sigma]2", "2"]}], ")"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      RowBox[{"4", " ", 
       SuperscriptBox["\[Sigma]2", "2"]}]}], ")"}], "2"]}]]], "Output",
 CellChangeTimes->{{3.8000111553201838`*^9, 3.800011158757802*^9}},
 CellLabel->
  "Out[413]=",ExpressionUUID->"c53a6126-bddd-4096-9867-75fec265d9e4"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"We", " ", 
    RowBox[{"see", ":", "\[IndentingNewLine]", " ", 
     SubscriptBox["Z", 
      RowBox[{"1", "/", "2", " "}]]}]}], "=", "  ", 
   RowBox[{
    RowBox[{
     SubscriptBox["\[CapitalZHacek]", "1"], "\[IndentingNewLine]", " ", 
     SubscriptBox["Z", "1"]}], "  ", "=", "  ", 
    SubscriptBox["\[CapitalZHacek]", "2"]}]}], "\[IndentingNewLine]", 
  "*)"}]], "Input",
 CellChangeTimes->{{3.8000110865753317`*^9, 3.8000112203154182`*^9}, {
  3.800019191482252*^9, 
  3.800019194815473*^9}},ExpressionUUID->"80b1b53a-7f7c-4a08-8086-\
13bab9d66284"],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{"3", "-", 
   RowBox[{"inst", " ", "check"}]}], "*)"}]], "Input",
 CellChangeTimes->{{3.8000106269529333`*^9, 
  3.8000106302575083`*^9}},ExpressionUUID->"d4e9b853-bba6-45e5-a5c3-\
f81099822238"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"Coefficient", "[", 
           RowBox[{
            RowBox[{"Coefficient", "[", 
             RowBox[{
              RowBox[{"Coefficient", "[", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], 
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{
                    RowBox[{"p", "^", "2"}], " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}]}], "-", 
                  RowBox[{
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", 
                    RowBox[{"1", "/", "2"}], ",", 
                    RowBox[{"1", "/", "2"}], ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{"p", " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}], "^", "2"}]}], ")"}],
                 ",", "\[Epsilon]1", ",", "k"}], "]"}], ",", "\[Epsilon]2", 
              ",", "l"}], "]"}], ",", "\[Xi]", ",", "m"}], "]"}], "//", 
          "Simplify"}], ")"}], "\[Equal]", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{"Coefficient", "[", 
             RowBox[{
              RowBox[{"Coefficient", "[", 
               RowBox[{
                RowBox[{"Coefficient", "[", 
                 RowBox[{
                  RowBox[{"(", 
                   RowBox[{
                    RowBox[{
                    RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", "0", ",", "0", ",", "t"}], "]"}], 
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", "0", ",", "0", ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{
                    RowBox[{"p", "^", "2"}], " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}]}], "-", 
                    RowBox[{
                    RowBox[{"(", 
                    RowBox[{
                    RowBox[{"TauC2", "[", 
                    RowBox[{
                    "\[Sigma]1", ",", "\[Sigma]2", ",", "\[Eta]1", ",", 
                    "\[Eta]2", ",", "0", ",", "0", ",", "t"}], "]"}], "/.", 
                    RowBox[{
                    RowBox[{"t", "^", "p_"}], " ", "\[RuleDelayed]", " ", 
                    RowBox[{"p", " ", 
                    RowBox[{"t", "^", "p"}]}]}]}], ")"}], "^", "2"}]}], ")"}],
                   ",", "\[Epsilon]1", ",", "k"}], "]"}], ",", "\[Epsilon]2", 
                ",", "l"}], "]"}], ",", "\[Xi]", ",", "m"}], "]"}], "//", 
            "Simplify"}], ")"}], "//", "Simplify"}], ")"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"k", ",", "0", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"l", ",", "0", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"m", ",", 
        RowBox[{"3", "/", "2"}], ",", 
        RowBox[{"3", "/", "2"}]}], "}"}]}], "]"}], "//", "Flatten"}], "//", 
   "DeleteDuplicates"}], "//", 
  RowBox[{"Simplify", "/.", 
   RowBox[{"t", "\[Rule]", "1"}]}]}]], "Input",
 CellChangeTimes->{{3.800010592711276*^9, 3.800010607458304*^9}},
 CellLabel->
  "In[396]:=",ExpressionUUID->"c64c06ea-f863-463e-9fd9-d75d0dca87a9"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    FractionBox["1", "4"], " ", 
    SuperscriptBox["t", 
     RowBox[{
      FractionBox["3", "2"], "+", 
      SuperscriptBox["\[Sigma]1", "2"], "+", 
      SuperscriptBox["\[Sigma]2", "2"]}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", 
          RowBox[{
           RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{"\[Sigma]1", ",", 
         RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", 
             RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", 
             RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", 
            RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], "-", 
      RowBox[{
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], 
       " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", 
             RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
           "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", 
             RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}]}], 
        ")"}]}], "+", 
      RowBox[{"4", " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
        ")"}]}], "+", 
      RowBox[{"4", " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], 
           "2"], " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], 
      "-", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "+", 
         RowBox[{"9", " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["3", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}]}], ")"}]}]}], 
     ")"}]}], "\[Equal]", "0"}], "}"}]], "Output",
 CellChangeTimes->{3.800010634008498*^9},
 CellLabel->
  "Out[396]=",ExpressionUUID->"a930255f-a580-48f3-be31-12813633e338"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"0", "==", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", 
          RowBox[{
           RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{"\[Sigma]1", ",", 
         RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", 
             RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", 
             RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", 
            RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], "-", 
      RowBox[{
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], 
       " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", 
             RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
           "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", 
             RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}]}], 
        ")"}]}], "+", 
      RowBox[{"4", " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
        ")"}]}], "+", 
      RowBox[{"4", " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          RowBox[{"-", 
           FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"F0", "[", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
         RowBox[{
          FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "1"}], "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], 
           "2"], " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
          " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
            RowBox[{
             FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], 
      "-", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["1", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], " ", 
          RowBox[{
           SubscriptBox["Z", "1"], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "+", 
         RowBox[{"9", " ", 
          RowBox[{
           SubscriptBox["Z", 
            FractionBox["3", "2"]], "[", 
           RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}]}], ")"}]}]}], 
     ")"}]}], ",", 
   RowBox[{
    SubscriptBox["Z", 
     FractionBox["3", "2"]], "[", 
    RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.8000106693013287`*^9, 3.800010689720606*^9}},
 CellLabel->
  "In[397]:=",ExpressionUUID->"a6e18503-cb18-4770-88d9-9469fa84af54"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     SubscriptBox["Z", 
      FractionBox["3", "2"]], "[", 
     RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "\[Rule]", 
    RowBox[{
     FractionBox["1", 
      RowBox[{"9", " ", 
       SuperscriptBox[
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]}]], 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1", ",", 
           RowBox[{
            RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{"\[Sigma]1", ",", 
          RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "-", 
              RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", 
              RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{"\[Sigma]1", ",", 
             RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], "-", 
       RowBox[{
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], 
        " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "-", 
              RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
            "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", 
              RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}]}]}], 
         ")"}]}], "-", 
       RowBox[{
        SuperscriptBox[
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
        RowBox[{
         SubscriptBox["Z", 
          FractionBox["1", "2"]], "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], " ", 
        RowBox[{
         SubscriptBox["Z", "1"], "[", 
         RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "+", 
       RowBox[{"4", " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
           " ", 
           RowBox[{
            SubscriptBox["Z", "1"], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], 
           " ", 
           RowBox[{
            SubscriptBox["Z", "1"], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
         ")"}]}], "+", 
       RowBox[{"4", " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"F0", "[", 
         RowBox[{
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
          RowBox[{
           FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
           RowBox[{
            SubscriptBox["Z", 
             FractionBox["1", "2"]], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}],
             "2"], " ", 
           RowBox[{
            SubscriptBox["Z", "1"], "[", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              RowBox[{"-", 
               FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], 
           " ", 
           RowBox[{
            SubscriptBox["Z", "1"], "[", 
            RowBox[{
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
             RowBox[{
              FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], 
         ")"}]}]}], ")"}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.800010690333806*^9},
 CellLabel->
  "Out[397]=",ExpressionUUID->"c7ccdc26-56dd-4410-aab1-f7144af91c5e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         FractionBox["1", 
          RowBox[{"9", " ", 
           SuperscriptBox[
            RowBox[{"F0", "[", 
             RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"]}]], 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             RowBox[{"F0", "[", 
              RowBox[{"\[Sigma]1", ",", 
               RowBox[{
                RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], " ", 
            RowBox[{"F0", "[", 
             RowBox[{"\[Sigma]1", ",", 
              RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "-", 
                  RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{"\[Sigma]1", ",", 
                 RowBox[{
                  RowBox[{"-", "1"}], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "+", 
                  RowBox[{"4", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{"\[Sigma]1", ",", 
                 RowBox[{"1", "+", "\[Sigma]2"}]}], "]"}]}]}], ")"}]}], "-", 
           RowBox[{
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
             "]"}], " ", 
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], "]"}], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "-", 
                  RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
                "]"}]}], "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "+", 
                  RowBox[{"4", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{"1", "+", "\[Sigma]1"}], ",", "\[Sigma]2"}], 
                "]"}]}]}], ")"}]}], "-", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"F0", "[", 
              RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "2"], " ", 
            RowBox[{
             SubscriptBox["Z", 
              FractionBox["1", "2"]], "[", 
             RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], " ", 
            RowBox[{
             SubscriptBox["Z", "1"], "[", 
             RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}]}], "+", 
           RowBox[{"4", " ", 
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], 
              "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], 
                "2"], " ", 
               RowBox[{
                SubscriptBox["Z", "1"], "[", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], ")"}], 
                "2"], " ", 
               RowBox[{
                SubscriptBox["Z", "1"], "[", 
                RowBox[{
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}]}], 
             ")"}]}], "+", 
           RowBox[{"4", " ", 
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               RowBox[{"-", 
                FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
            RowBox[{"F0", "[", 
             RowBox[{
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
              RowBox[{
               FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}], " ", 
               
               RowBox[{
                SubscriptBox["Z", 
                 FractionBox["1", "2"]], "[", 
                RowBox[{
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}], "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{"-", "1"}], "+", "\[Sigma]1", "+", "\[Sigma]2"}], 
                 ")"}], "2"], " ", 
               RowBox[{
                SubscriptBox["Z", "1"], "[", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  RowBox[{"-", 
                   FractionBox["1", "2"]}], "+", "\[Sigma]2"}]}], "]"}]}], 
              "+", 
              RowBox[{
               SuperscriptBox[
                RowBox[{"(", 
                 RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], ")"}], 
                "2"], " ", 
               RowBox[{
                SubscriptBox["Z", "1"], "[", 
                RowBox[{
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]1"}], ",", 
                 RowBox[{
                  FractionBox["1", "2"], "+", "\[Sigma]2"}]}], "]"}]}]}], 
             ")"}]}]}], ")"}]}], "/.", " ", 
        RowBox[{
         RowBox[{"F0", "[", 
          RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", 
         RowBox[{"1", "/", 
          RowBox[{"Abs", "[", 
           RowBox[{
            RowBox[{"G", "[", 
             RowBox[{"1", "-", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "+", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "-", 
              RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "+", 
              RowBox[{"2", "\[Sigma]2"}]}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "-", 
              RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "+", 
              RowBox[{"2", "\[Sigma]1"}]}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "-", "\[Sigma]1", "-", "\[Sigma]2"}], "]"}], 
            RowBox[{"G", "[", 
             RowBox[{"1", "+", "\[Sigma]1", "+", "\[Sigma]2"}], "]"}]}], 
           "]"}]}]}]}], "/.", 
       RowBox[{
        RowBox[{
         SubscriptBox["Z", 
          RowBox[{"1", "/", "2"}]], "[", 
         RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", " ", 
        FractionBox["1", 
         RowBox[{"2", " ", 
          SuperscriptBox["\[Sigma]1", "2"], " ", 
          SuperscriptBox["\[Sigma]2", "2"]}]]}]}], "/.", 
      RowBox[{
       RowBox[{
        SubscriptBox["Z", "1"], "[", 
        RowBox[{"\[Sigma]1_", ",", "\[Sigma]2_"}], "]"}], "\[Rule]", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[Sigma]1", "2"], "-", 
         RowBox[{"8", " ", 
          SuperscriptBox["\[Sigma]1", "4"]}], "+", 
         RowBox[{"16", " ", 
          SuperscriptBox["\[Sigma]1", "6"]}], "+", 
         SuperscriptBox["\[Sigma]2", "2"], "+", 
         RowBox[{"128", " ", 
          SuperscriptBox["\[Sigma]1", "6"], " ", 
          SuperscriptBox["\[Sigma]2", "2"]}], "-", 
         RowBox[{"8", " ", 
          SuperscriptBox["\[Sigma]2", "4"]}], "-", 
         RowBox[{"256", " ", 
          SuperscriptBox["\[Sigma]1", "4"], " ", 
          SuperscriptBox["\[Sigma]2", "4"]}], "+", 
         RowBox[{"16", " ", 
          SuperscriptBox["\[Sigma]2", "6"]}], "+", 
         RowBox[{"128", " ", 
          SuperscriptBox["\[Sigma]1", "2"], " ", 
          SuperscriptBox["\[Sigma]2", "6"]}]}], 
        RowBox[{"4", " ", 
         SuperscriptBox["\[Sigma]1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "+", 
            RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"1", "+", 
            RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
         SuperscriptBox["\[Sigma]2", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "+", 
            RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"1", "+", 
            RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"]}]]}]}], "//.", 
     RowBox[{
      RowBox[{"Abs", "[", 
       RowBox[{"x_", " ", "y_"}], " ", "]"}], "\[Rule]", " ", 
      RowBox[{
       RowBox[{"Abs", "[", "x", "]"}], 
       RowBox[{"Abs", "[", "y", "]"}]}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Sigma]1", " ", ">", "0"}], ",", " ", 
      RowBox[{"\[Sigma]2", " ", ">", "0"}]}], "}"}]}], "]"}], "//", 
  "Together"}]], "Input",
 CellChangeTimes->{{3.800010693054743*^9, 3.800010764287889*^9}, {
  3.8000192109369497`*^9, 3.800019221142683*^9}},
 CellLabel->
  "In[480]:=",ExpressionUUID->"74f7cd58-4834-4c9a-840a-f5762cd8b6bf"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"3", " ", 
     SuperscriptBox["\[Sigma]1", "2"]}], "+", 
    RowBox[{"43", " ", 
     SuperscriptBox["\[Sigma]1", "4"]}], "-", 
    RowBox[{"88", " ", 
     SuperscriptBox["\[Sigma]1", "6"]}], "+", 
    RowBox[{"48", " ", 
     SuperscriptBox["\[Sigma]1", "8"]}], "+", 
    RowBox[{"3", " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"146", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "+", 
    RowBox[{"187", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"24", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"80", " ", 
     SuperscriptBox["\[Sigma]1", "8"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "+", 
    RowBox[{"43", " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"187", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "-", 
    RowBox[{"288", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "8"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "-", 
    RowBox[{"88", " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "-", 
    RowBox[{"24", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "-", 
    RowBox[{"256", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "+", 
    RowBox[{"48", " ", 
     SuperscriptBox["\[Sigma]2", "8"]}], "-", 
    RowBox[{"80", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "8"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "8"]}]}], ")"}], "/", 
  RowBox[{"(", 
   RowBox[{"24", " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ")"}], "2"], " ", 
    SuperscriptBox["\[Sigma]1", "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", "\[Sigma]1"}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Sigma]2"}], ")"}], "2"], " ", 
    SuperscriptBox["\[Sigma]2", "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.800010759700048*^9, 3.8000107799463787`*^9}, 
   3.8000192258919277`*^9},
 CellLabel->
  "Out[480]=",ExpressionUUID->"1df7b630-a095-4a33-99b2-1d434dec42c8"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   SubscriptBox["\[CapitalZHacek]", 
    RowBox[{"3", "/", "2"}]], "[", 
   RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "//", 
  "Together"}]], "Input",
 CellChangeTimes->{{3.8000107958831367`*^9, 3.8000108155840197`*^9}, 
   3.8000192298162613`*^9},
 CellLabel->
  "In[481]:=",ExpressionUUID->"21675480-bb3f-48d0-aa73-60cfa7b21c56"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"3", " ", 
     SuperscriptBox["\[Sigma]1", "2"]}], "+", 
    RowBox[{"43", " ", 
     SuperscriptBox["\[Sigma]1", "4"]}], "-", 
    RowBox[{"88", " ", 
     SuperscriptBox["\[Sigma]1", "6"]}], "+", 
    RowBox[{"48", " ", 
     SuperscriptBox["\[Sigma]1", "8"]}], "+", 
    RowBox[{"3", " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"146", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "+", 
    RowBox[{"187", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"24", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "-", 
    RowBox[{"80", " ", 
     SuperscriptBox["\[Sigma]1", "8"], " ", 
     SuperscriptBox["\[Sigma]2", "2"]}], "+", 
    RowBox[{"43", " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"187", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "-", 
    RowBox[{"288", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "8"], " ", 
     SuperscriptBox["\[Sigma]2", "4"]}], "-", 
    RowBox[{"88", " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "-", 
    RowBox[{"24", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "-", 
    RowBox[{"256", " ", 
     SuperscriptBox["\[Sigma]1", "6"], " ", 
     SuperscriptBox["\[Sigma]2", "6"]}], "+", 
    RowBox[{"48", " ", 
     SuperscriptBox["\[Sigma]2", "8"]}], "-", 
    RowBox[{"80", " ", 
     SuperscriptBox["\[Sigma]1", "2"], " ", 
     SuperscriptBox["\[Sigma]2", "8"]}], "+", 
    RowBox[{"128", " ", 
     SuperscriptBox["\[Sigma]1", "4"], " ", 
     SuperscriptBox["\[Sigma]2", "8"]}]}], ")"}], "/", 
  RowBox[{"(", 
   RowBox[{"24", " ", 
    SuperscriptBox["\[Sigma]1", "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       SuperscriptBox["\[Sigma]1", "2"]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"4", " ", 
        SuperscriptBox["\[Sigma]1", "2"]}]}], ")"}], "2"], " ", 
    SuperscriptBox["\[Sigma]2", "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["\[Sigma]1", "2"], "-", 
       SuperscriptBox["\[Sigma]2", "2"]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       SuperscriptBox["\[Sigma]2", "2"]}], ")"}], "2"], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"4", " ", 
        SuperscriptBox["\[Sigma]2", "2"]}]}], ")"}], "2"]}], 
   ")"}]}]], "Output",
 CellChangeTimes->{{3.800010799992099*^9, 3.800010816192299*^9}, 
   3.800019230510179*^9},
 CellLabel->
  "Out[481]=",ExpressionUUID->"87084165-1801-4853-9018-8d3d46077203"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalZHacek]", 
     RowBox[{"3", "/", "2"}]], "[", 
    RowBox[{"\[Sigma]1", ",", "\[Sigma]2"}], "]"}], "-", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"3", " ", 
       SuperscriptBox["\[Sigma]1", "2"]}], "+", 
      RowBox[{"43", " ", 
       SuperscriptBox["\[Sigma]1", "4"]}], "-", 
      RowBox[{"88", " ", 
       SuperscriptBox["\[Sigma]1", "6"]}], "+", 
      RowBox[{"48", " ", 
       SuperscriptBox["\[Sigma]1", "8"]}], "+", 
      RowBox[{"3", " ", 
       SuperscriptBox["\[Sigma]2", "2"]}], "-", 
      RowBox[{"146", " ", 
       SuperscriptBox["\[Sigma]1", "2"], " ", 
       SuperscriptBox["\[Sigma]2", "2"]}], "+", 
      RowBox[{"187", " ", 
       SuperscriptBox["\[Sigma]1", "4"], " ", 
       SuperscriptBox["\[Sigma]2", "2"]}], "-", 
      RowBox[{"24", " ", 
       SuperscriptBox["\[Sigma]1", "6"], " ", 
       SuperscriptBox["\[Sigma]2", "2"]}], "-", 
      RowBox[{"80", " ", 
       SuperscriptBox["\[Sigma]1", "8"], " ", 
       SuperscriptBox["\[Sigma]2", "2"]}], "+", 
      RowBox[{"43", " ", 
       SuperscriptBox["\[Sigma]2", "4"]}], "+", 
      RowBox[{"187", " ", 
       SuperscriptBox["\[Sigma]1", "2"], " ", 
       SuperscriptBox["\[Sigma]2", "4"]}], "-", 
      RowBox[{"288", " ", 
       SuperscriptBox["\[Sigma]1", "4"], " ", 
       SuperscriptBox["\[Sigma]2", "4"]}], "+", 
      RowBox[{"128", " ", 
       SuperscriptBox["\[Sigma]1", "6"], " ", 
       SuperscriptBox["\[Sigma]2", "4"]}], "+", 
      RowBox[{"128", " ", 
       SuperscriptBox["\[Sigma]1", "8"], " ", 
       SuperscriptBox["\[Sigma]2", "4"]}], "-", 
      RowBox[{"88", " ", 
       SuperscriptBox["\[Sigma]2", "6"]}], "-", 
      RowBox[{"24", " ", 
       SuperscriptBox["\[Sigma]1", "2"], " ", 
       SuperscriptBox["\[Sigma]2", "6"]}], "+", 
      RowBox[{"128", " ", 
       SuperscriptBox["\[Sigma]1", "4"], " ", 
       SuperscriptBox["\[Sigma]2", "6"]}], "-", 
      RowBox[{"256", " ", 
       SuperscriptBox["\[Sigma]1", "6"], " ", 
       SuperscriptBox["\[Sigma]2", "6"]}], "+", 
      RowBox[{"48", " ", 
       SuperscriptBox["\[Sigma]2", "8"]}], "-", 
      RowBox[{"80", " ", 
       SuperscriptBox["\[Sigma]1", "2"], " ", 
       SuperscriptBox["\[Sigma]2", "8"]}], "+", 
      RowBox[{"128", " ", 
       SuperscriptBox["\[Sigma]1", "4"], " ", 
       SuperscriptBox["\[Sigma]2", "8"]}]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{"24", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", "\[Sigma]1"}], ")"}], "2"], " ", 
      SuperscriptBox["\[Sigma]1", "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "+", "\[Sigma]1"}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", 
         RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "+", 
         RowBox[{"2", " ", "\[Sigma]1"}]}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"\[Sigma]1", "-", "\[Sigma]2"}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", "\[Sigma]2"}], ")"}], "2"], " ", 
      SuperscriptBox["\[Sigma]2", "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"\[Sigma]1", "+", "\[Sigma]2"}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", 
         RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "+", 
         RowBox[{"2", " ", "\[Sigma]2"}]}], ")"}], "2"]}], ")"}]}]}], "//", 
  "Simplify"}]], "Input",
 CellChangeTimes->{{3.8000108264941387`*^9, 3.800010828632773*^9}, {
  3.80001924406886*^9, 3.800019252816103*^9}},
 CellLabel->
  "In[482]:=",ExpressionUUID->"cceea6cd-339a-4505-b88d-304f7f1ce235"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.800010828965386*^9, 3.8000192536239758`*^9},
 CellLabel->
  "Out[482]=",ExpressionUUID->"abec6ea6-4d66-4835-875e-5a831469dd00"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"So", " ", 
    SubscriptBox["Z", "3"]}], " ", "=", " ", 
   SubscriptBox["\[CapitalZHacek]", 
    RowBox[{"3", "/", "2"}]]}], "*)"}]], "Input",
 CellChangeTimes->{{3.8000112528874693`*^9, 3.800011277454385*^9}, 
   3.8000192565641737`*^9},ExpressionUUID->"9d64c01d-637b-4a7a-9832-\
4be3136a987f"]
},
WindowSize->{1920, 1037},
WindowMargins->{{0, Automatic}, {Automatic, 18}},
Magnification:>1.5 Inherited,
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 5286, 165, 516, "Input",ExpressionUUID->"7fbbfe53-669a-4751-a8c1-45b12bcf4019"],
Cell[5847, 187, 2872, 84, 116, "Input",ExpressionUUID->"13ba7768-eb8f-4690-9f95-b9283709dfb4"],
Cell[CellGroupData[{
Cell[8744, 275, 2065, 61, 121, "Input",ExpressionUUID->"33ccae59-5abe-41fa-8607-c77230430fb8"],
Cell[10812, 338, 273, 4, 53, "Output",ExpressionUUID->"89e495a0-01a9-4c0c-9f80-8ec3c2549d50"]
}, Open  ]],
Cell[11100, 345, 3261, 95, 263, "Input",ExpressionUUID->"cbf7f7ef-2308-4799-a4df-dc52a26115cb"],
Cell[14364, 442, 181, 4, 47, "Input",ExpressionUUID->"69b8ce18-ed8a-4a71-ac1a-926da1fb788d"],
Cell[14548, 448, 9002, 236, 456, "Input",ExpressionUUID->"7886a0f0-8552-4412-8237-ebbaff04e0a2"],
Cell[CellGroupData[{
Cell[23575, 688, 8432, 220, 456, "Input",ExpressionUUID->"2ff49383-25ea-4cad-bf7e-4594c863785b"],
Cell[32010, 910, 228, 4, 53, "Output",ExpressionUUID->"27a4126f-4994-46ed-9363-b23e5e86955d"]
}, Open  ]],
Cell[32253, 917, 8201, 217, 422, "Input",ExpressionUUID->"2f73a5d0-6189-4400-a3fc-d8144dfe2a7d"],
Cell[40457, 1136, 9195, 242, 490, "Input",ExpressionUUID->"32e8d142-a8ce-41f0-8b8b-3291527c7e12"],
Cell[49655, 1380, 205, 4, 116, "Input",ExpressionUUID->"ff50421e-fde3-4253-863c-6965bed59fe0"],
Cell[49863, 1386, 3313, 91, 227, "Input",ExpressionUUID->"a8599c4e-acff-44f7-956a-bde13bbd1df1",
 InitializationCell->True],
Cell[53179, 1479, 3063, 88, 203, "Input",ExpressionUUID->"802de681-664f-4d0f-980f-7425f7151347"],
Cell[56245, 1569, 476, 12, 47, "Input",ExpressionUUID->"bcbb43e4-508a-4b68-89ed-b456116017b1"],
Cell[CellGroupData[{
Cell[56746, 1585, 6378, 141, 310, "Input",ExpressionUUID->"4f5b7f81-b6c1-4e7e-ad7b-caaacf32513c",
 InitializationCell->True],
Cell[63127, 1728, 176, 2, 53, "Output",ExpressionUUID->"d6f3e6d5-b07e-4620-888b-a7e32473ec5e"]
}, Open  ]],
Cell[63318, 1733, 509, 12, 47, "Input",ExpressionUUID->"8f201223-6022-4d60-9d7c-ee65f3f5b89c"],
Cell[CellGroupData[{
Cell[63852, 1749, 2692, 76, 234, "Input",ExpressionUUID->"1529a074-4d71-4fee-962f-1a6fa3e302b5"],
Cell[66547, 1827, 230, 5, 53, "Output",ExpressionUUID->"f4fb59ed-aae5-44b9-a818-f5a432273fc1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[66814, 1837, 2151, 63, 124, "Input",ExpressionUUID->"e6b6797e-fb4f-42c9-a544-a7d78b436a9f"],
Cell[68968, 1902, 3950, 113, 200, "Output",ExpressionUUID->"cfcb0b49-acdb-4be3-8d09-34b95f8a15c6"]
}, Open  ]],
Cell[72933, 2018, 221, 5, 47, "Input",ExpressionUUID->"946a178e-81ac-482b-bf35-1aa0522c4009"],
Cell[CellGroupData[{
Cell[73179, 2027, 5503, 151, 338, "Input",ExpressionUUID->"dd30d338-df56-4756-b60d-bfbc791cd396"],
Cell[78685, 2180, 532, 11, 77, "Output",ExpressionUUID->"00d4c3bf-2069-4123-afe6-e994f3ee4246"]
}, Open  ]],
Cell[79232, 2194, 223, 5, 47, "Input",ExpressionUUID->"75eeb948-90e1-4478-8c7d-8cdca2ea5520"],
Cell[CellGroupData[{
Cell[79480, 2203, 5054, 143, 242, "Input",ExpressionUUID->"bc14fa6c-3d3e-4134-afbc-1ec3075c4b2e"],
Cell[84537, 2348, 4873, 138, 203, "Output",ExpressionUUID->"33980c37-0ec3-4974-9f89-8fe7ac937c50"]
}, Open  ]],
Cell[CellGroupData[{
Cell[89447, 2491, 7079, 188, 356, "Input",ExpressionUUID->"33a9b55e-cc96-47b8-8a78-b9fab64cb29d"],
Cell[96529, 2681, 1876, 54, 86, "Output",ExpressionUUID->"b5007431-c6c7-441c-868e-85af1934780d"]
}, Open  ]],
Cell[98420, 2738, 265, 7, 47, "Input",ExpressionUUID->"df0aed34-95e2-4d53-830e-11f7801f2206"],
Cell[98688, 2747, 5083, 157, 477, "Input",ExpressionUUID->"6ab92e69-3298-4e5d-8c38-8c47a9b03d0d",
 InitializationCell->True],
Cell[CellGroupData[{
Cell[103796, 2908, 317, 8, 47, "Input",ExpressionUUID->"de09ef28-b5cc-4eaf-8c57-76e9a86981bb"],
Cell[104116, 2918, 1505, 44, 92, "Output",ExpressionUUID->"c53a6126-bddd-4096-9867-75fec265d9e4"]
}, Open  ]],
Cell[105636, 2965, 610, 16, 150, "Input",ExpressionUUID->"80b1b53a-7f7c-4a08-8086-13bab9d66284"],
Cell[106249, 2983, 235, 6, 47, "Input",ExpressionUUID->"d4e9b853-bba6-45e5-a5c3-f81099822238"],
Cell[CellGroupData[{
Cell[106509, 2993, 4617, 109, 218, "Input",ExpressionUUID->"c64c06ea-f863-463e-9fd9-d75d0dca87a9"],
Cell[111129, 3104, 7807, 233, 318, "Output",ExpressionUUID->"a930255f-a580-48f3-be31-12813633e338"]
}, Open  ]],
Cell[CellGroupData[{
Cell[118973, 3342, 7766, 231, 476, "Input",ExpressionUUID->"a6e18503-cb18-4770-88d9-9469fa84af54"],
Cell[126742, 3575, 7851, 228, 320, "Output",ExpressionUUID->"c7ccdc26-56dd-4410-aab1-f7144af91c5e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[134630, 3808, 12598, 331, 528, "Input",ExpressionUUID->"74f7cd58-4834-4c9a-840a-f5762cd8b6bf"],
Cell[147231, 4141, 3655, 104, 133, "Output",ExpressionUUID->"1df7b630-a095-4a33-99b2-1d434dec42c8"]
}, Open  ]],
Cell[CellGroupData[{
Cell[150923, 4250, 372, 10, 47, "Input",ExpressionUUID->"21675480-bb3f-48d0-aa73-60cfa7b21c56"],
Cell[151298, 4262, 3282, 94, 95, "Output",ExpressionUUID->"87084165-1801-4853-9018-8d3d46077203"]
}, Open  ]],
Cell[CellGroupData[{
Cell[154617, 4361, 4065, 111, 162, "Input",ExpressionUUID->"cceea6cd-339a-4505-b88d-304f7f1ce235"],
Cell[158685, 4474, 177, 3, 53, "Output",ExpressionUUID->"abec6ea6-4d66-4835-875e-5a831469dd00"]
}, Open  ]],
Cell[158877, 4480, 349, 9, 47, "Input",ExpressionUUID->"9d64c01d-637b-4a7a-9832-4be3136a987f"]
}
]
*)