(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)
Echo@"\!\(\*
StyleBox[\"Warning\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\":\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"On\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"Sep\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"4\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"2019\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"I\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"swapped\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"the\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"operations\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"\[Epsilon]\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"and\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"\[Eta]\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\".\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"Some\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"incompatibilities\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"may\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"arise\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"in\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"older\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"notebooks\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\".\",\nFontColor->RGBColor[1, 0, 0]]\)"


(* ::Input::Initialization:: *)
Subscript[sm, i_,j_->k_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[Subscript[b, k](Subscript[\[Beta], i]+Subscript[\[Beta], j])+Subscript[t, k](Subscript[\[Tau], i]+Subscript[\[Tau], j])+Subscript[a, k](Subscript[\[Alpha], i]+Subscript[\[Alpha], j])+Subscript[y, k](Subscript[\[Eta], i]+Subscript[\[Eta], j])+Subscript[x, k](Subscript[\[Xi], i]+Subscript[\[Xi], j])];
Subscript[s\[CapitalDelta], i_->j_,k_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {j, k}\)]\)[Subscript[\[Beta], i](Subscript[b, j]+Subscript[b, k])+Subscript[\[Tau], i](Subscript[t, j]+Subscript[t, k])+Subscript[\[Alpha], i](Subscript[a, j]+Subscript[a, k])+Subscript[\[Eta], i](Subscript[y, j]+Subscript[y, k])+Subscript[\[Xi], i](Subscript[x, j]+Subscript[x, k])];
Subscript[sS, i_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[-Subscript[\[Beta], i] Subscript[b, i]-Subscript[\[Tau], i] Subscript[t, i]-Subscript[\[Alpha], i] Subscript[a, i]-Subscript[\[Eta], i] Subscript[y, i]-Subscript[\[Xi], i] Subscript[x, i]];
Subscript[s\[Eta], i_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0];Subscript[s\[Epsilon], i_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {}\)]\)[0];


(* ::Input::Initialization:: *)
Subscript[s\[Sigma], i_->j_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {j}\)]\)[Subscript[\[Beta], i] Subscript[b, j]+Subscript[\[Tau], i] Subscript[t, j]+Subscript[\[Alpha], i] Subscript[a, j]+Subscript[\[Eta], i] Subscript[y, j]+Subscript[\[Xi], i] Subscript[x, j]];
Subscript[s\[CapitalUpsilon], i_->j_,k_,l_,m_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {j, k, l, m}\)]\)[Subscript[\[Beta], i] Subscript[b, k]+Subscript[\[Tau], i] Subscript[t, k]+Subscript[\[Alpha], i] Subscript[a, l]+Subscript[\[Eta], i] Subscript[y, j]+Subscript[\[Xi], i] Subscript[x, m]];


(* ::Input::Initialization:: *)
c\[CapitalLambda]=(Subscript[\[Eta], i]+(E^(-\[Gamma] Subscript[\[Alpha], i]-\[Epsilon] Subscript[\[Beta], i]) Subscript[\[Eta], j])/(1+\[Gamma] \[Epsilon] Subscript[\[Eta], j] Subscript[\[Xi], i]))Subscript[y, k]+(Subscript[\[Beta], i]+Subscript[\[Beta], j]+Log[1+\[Gamma] \[Epsilon] Subscript[\[Eta], j] Subscript[\[Xi], i]]/\[Epsilon])Subscript[b, k]+(Subscript[\[Alpha], i]+Subscript[\[Alpha], j]+Log[1+\[Gamma] \[Epsilon] Subscript[\[Eta], j] Subscript[\[Xi], i]]/\[Gamma])Subscript[a, k]+((E^(-\[Gamma] Subscript[\[Alpha], j]-\[Epsilon] Subscript[\[Beta], j]) Subscript[\[Xi], i])/(1+\[Gamma] \[Epsilon] Subscript[\[Eta], j] Subscript[\[Xi], i])+Subscript[\[Xi], j])Subscript[x, k];
Define[Subscript[cm, i,j->k]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[c\[CapitalLambda]]]


(* ::Input::Initialization:: *)
Define[Subscript[c\[Sigma], i->j]=Subscript[s\[Sigma], i,j]/.Subscript[\[Tau], i]->0,Subscript[c\[Epsilon], i]=Subscript[s\[Epsilon], i], Subscript[c\[Eta], i]=Subscript[s\[Eta], i],Subscript[c\[CapitalDelta], i->j,k]=Subscript[s\[CapitalDelta], i->j,k],
Subscript[cS, i]=Subscript[sS, i]//Subscript[s\[CapitalUpsilon], i->1,2,3,4]//Subscript[cm, 4,3->i]//Subscript[cm, i,2->i]//Subscript[cm, i,1->i]];


(* ::Input::Initialization:: *)
Define[Subscript[a\[Sigma], i->j]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {j}\)]\)[Subscript[a, j] Subscript[\[Alpha], i]+Subscript[x, j] Subscript[\[Xi], i]],Subscript[b\[Sigma], i->j]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {j}\)]\)[Subscript[b, j] Subscript[\[Beta], i]+Subscript[y, j] Subscript[\[Eta], i]]]


(* ::Input::Initialization:: *)
Define[Subscript[am, i,j->k]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[(Subscript[\[Alpha], i]+Subscript[\[Alpha], j])Subscript[a, k]+(\!\(
\*SubsuperscriptBox[\(\[ScriptCapitalA]\), \(j\), \(-1\)] 
\*SubscriptBox[\(\[Xi]\), \(i\)]\)+Subscript[\[Xi], j])Subscript[x, k]],
Subscript[bm, i,j->k]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[(Subscript[\[Beta], i]+Subscript[\[Beta], j])Subscript[b, k]+(Subscript[\[Eta], i]+E^(- \[Epsilon] Subscript[\[Beta], i]) Subscript[\[Eta], j])Subscript[y, k]]]


(* ::Input::Initialization:: *)
Define[Subscript[R, i,j]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[\[HBar] Subscript[a, j] Subscript[b, i]+\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \($k + 1\)]\ 
\*FractionBox[\(
\*SuperscriptBox[\((1 - 
\*SuperscriptBox[\(E\), \(\[Gamma]\ \[Epsilon]\ \[HBar]\)])\), \(k\)] 
\*SuperscriptBox[\((\[HBar]\ 
\*SubscriptBox[\(y\), \(i\)] 
\*SubscriptBox[\(x\), \(j\)])\), \(k\)]\), \(k \((1 - 
\*SuperscriptBox[\(E\), \(k\ \[Gamma]\ \[Epsilon]\ \[HBar]\)])\)\)]\)],
Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]=CF@\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[-\[HBar] Subscript[a, j] Subscript[b, i],-\[HBar] Subscript[x, j] Subscript[y, i]/Subscript[B, i],1+If[$k==0, 0,Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(R\), \(_\)], \({i, j}, $k - 1\)]\)), $k][3]-
((Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(R\), \(_\)], \({i, j}, 0\)]\)), $k] Subscript[R, 1,2] Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(R\), \(_\)], \({3, 4}, $k - 1\)]\)), $k])//(Subscript[bm, i,1->i] Subscript[am, j,2->j])//(Subscript[bm, i,3->i] Subscript[am, j,4->j]))[3]]],
Subscript[P, i,j]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {}\)]\)[Subscript[\[Beta], i]Subscript[\[Alpha], j]/\[HBar],Subscript[\[Eta], i]Subscript[\[Xi], j]/\[HBar],1+If[$k==0,0,Subscript[(\!\(\*SubscriptBox[\(P\), \({i, j}, $k - 1\)]\)), $k][3]-
(Subscript[R, 1,2]//(Subscript[(\!\(\*SubscriptBox[\(P\), \({1, j}, 0\)]\)), $k] Subscript[(\!\(\*SubscriptBox[\(P\), \({i, 2}, $k - 1\)]\)), $k]))[3]]]]


(* ::Input::Initialization:: *)
Define[Subscript[aS, i]=(Subscript[a\[Sigma], i->2] Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), 1,i])//Subscript[P, 1,2],
Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[-Subscript[a, i] Subscript[\[Alpha], i],-Subscript[x, i] Subscript[\[ScriptCapitalA], i] Subscript[\[Xi], i],1+If[$k==0, 0,Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, $k - 1\)]\)), $k][3]-
(Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, 0\)]\)), $k]//Subscript[aS, i]//Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, $k - 1\)]\)), $k])[3]]]]


(* ::Input::Initialization:: *)
Define[Subscript[bS, i]=Subscript[b\[Sigma], i->1] Subscript[R, i,2]//Subscript[aS, 2]//Subscript[P, 1,2],
Subscript[\!\(\*OverscriptBox[\(bS\), \(_\)]\), i]=Subscript[b\[Sigma], i->1] Subscript[R, i,2]//Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 2]//Subscript[P, 1,2],
Subscript[a\[CapitalDelta], i->j,k]=(Subscript[R, 1,j] Subscript[R, 2,k])//Subscript[bm, 1,2->3]//Subscript[P, 3,i],
Subscript[b\[CapitalDelta], i->j,k]=(Subscript[R, j,1] Subscript[R, k,2])//Subscript[am, 1,2->3]//Subscript[P, i,3]]


(* ::Input::Initialization:: *)
Define[Subscript[dm, i,j->k]=((Subscript[s\[CapitalUpsilon], i->4,4,1,1]//Subscript[a\[CapitalDelta], 1->1,2]//Subscript[a\[CapitalDelta], 2->2,3]//Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 3])(Subscript[s\[CapitalUpsilon], j->-1,-1,-4,-4]//Subscript[b\[CapitalDelta], -1->-1,-2]//Subscript[b\[CapitalDelta], -2->-2,-3]))//(Subscript[P, -1,3] Subscript[P, -3,1] Subscript[am, 2,-4->k] Subscript[bm, 4,-2->k])]


(* ::Input::Initialization:: *)
Define[Subscript[d\[Sigma], i->j]=Subscript[a\[Sigma], i->j] Subscript[b\[Sigma], i->j],
Subscript[d\[Epsilon], i]=Subscript[s\[Epsilon], i], Subscript[d\[Eta], i]=Subscript[s\[Eta], i],
Subscript[dS, i]=Subscript[s\[CapitalUpsilon], i->1,1,2,2]//(Subscript[\!\(\*OverscriptBox[\(bS\), \(_\)]\), 1] Subscript[aS, 2])//Subscript[dm, 2,1->i],
Subscript[\!\(\*OverscriptBox[\(dS\), \(_\)]\), i]=Subscript[s\[CapitalUpsilon], i->1,1,2,2]//(Subscript[bS, 1] Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 2])//Subscript[dm, 2,1->i],
Subscript[d\[CapitalDelta], i->j,k]=(Subscript[b\[CapitalDelta], i->3,1] Subscript[a\[CapitalDelta], i->2,4])//(Subscript[dm, 3,4->k] Subscript[dm, 1,2->j])]


(* ::Input::Initialization:: *)
Define[Subscript[C, i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0,0,\!\(
\*SubsuperscriptBox[\(B\), \(i\), \(1/2\)] 
\*SuperscriptBox[\(E\), \(\(-\[HBar]\)\ \[Epsilon]\ 
\*SubscriptBox[\(a\), \(i\)]/2\)]\)], $k],
Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0,0,\!\(
\*SubsuperscriptBox[\(B\), \(i\), \(\(-1\)/2\)] 
\*SuperscriptBox[\(E\), \(\[HBar]\ \[Epsilon]\ 
\*SubscriptBox[\(a\), \(i\)]/2\)]\)], $k],
Subscript[Kink, i] = (Subscript[R, 1,3] Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), 2])//Subscript[dm, 1,2->1]//Subscript[dm, 1,3->i],
Subscript[\!\(\*OverscriptBox[\(Kink\), \(_\)]\), i] = (Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), 1,3] Subscript[C, 2])//Subscript[dm, 1,2->1]//Subscript[dm, 1,3->i]]


(* ::Input::Initialization:: *)
Define[Subscript[b2t, i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[Subscript[\[Alpha], i] Subscript[a, i]+Subscript[\[Beta], i](\[Epsilon] Subscript[a, i]-Subscript[t, i])/\[Gamma]+Subscript[\[Xi], i] Subscript[x, i]+Subscript[\[Eta], i] Subscript[y, i]],
Subscript[t2b, i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[Subscript[\[Alpha], i] Subscript[a, i]+Subscript[\[Tau], i](\[Epsilon] Subscript[a, i]-\[Gamma] Subscript[b, i])+Subscript[\[Xi], i] Subscript[x, i]+Subscript[\[Eta], i] Subscript[y, i]]]


(* ::Input::Initialization:: *)
Define[Subscript[kR, i,j]=(Subscript[R, i,j]//(Subscript[b2t, i] Subscript[b2t, j])) /. Subscript[t, i|j]->t,
Subscript[\!\(\*OverscriptBox[\(kR\), \(_\)]\), i,j]=(Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]//(Subscript[b2t, i] Subscript[b2t, j])) /. {Subscript[t, i|j]->t,Subscript[T, i|j]->T},
Subscript[km, i,j->k]=((Subscript[t2b, i] Subscript[t2b, j])//Subscript[dm, i,j->k]//Subscript[b2t, k] )/. {Subscript[t, k]->t, Subscript[T, k]->T,Subscript[\[Tau], i|j]->0},
Subscript[kC, i]=(Subscript[C, i]//Subscript[b2t, i]) /. Subscript[T, i]->T,
Subscript[\!\(\*OverscriptBox[\(kC\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i]//Subscript[b2t, i])/. Subscript[T, i]->T,
Subscript[kKink, i]=(Subscript[Kink, i]//Subscript[b2t, i]) /. {Subscript[t, i]->t, Subscript[T, i]->T},
Subscript[\!\(\*OverscriptBox[\(kKink\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(Kink\), \(_\)]\), i]//Subscript[b2t, i]) /. {Subscript[t, i]->t, Subscript[T, i]->T}]
