(* ::Package:: *)

(************************************************************************)\012(* This file was generated automatically by the Mathematica front end.  *)\012(* It contains Initialization cells from a Notebook file, which         *)\012(* typically will have the same name as this file except ending in      *)\012(* ".nb" instead of ".m".                                               *)\012(*                                                                      *)\012(* This file is intended to be loaded into the Mathematica kernel using *)\012(* the package loading commands Get or Needs.  Doing so is equivalent   *)\012(* to using the Evaluate Initialization Cells menu command in the front *)\012(* end.                                                                 *)\012(*                                                                      *)\012(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)\012(* automatically each time the parent Notebook file is saved in the     *)\012(* Mathematica front end.  Any changes you make to this file will be    *)\012(* overwritten.                                                         *)\012(************************************************************************)\012\012

(* ::Input::Initialization:: *)
HL[\[ScriptCapitalE]_] := Style[\[ScriptCapitalE], Background -> Yellow];


(* ::Input::Initialization:: *)
MaxBy[list_,fun_,n_]:=list[[Ordering[fun/@list,-n]]];


(* ::Input::Initialization:: *)
CCF[\[ScriptCapitalE]_] := Subscript[PP, CCF]@ExpandDenominator@ExpandNumerator@Subscript[PP, Together]@Together[Subscript[PP, Exp][
Expand[\[ScriptCapitalE]] //. E^x_ E^y_:>E^(x+y) /. E^x_:>E^CCF[x]]];
CF[\[ScriptCapitalE]_List]:=CF/@\[ScriptCapitalE];
CF[sd_SeriesData] := MapAt[CF,sd,3];
CF[\[ScriptCapitalE]_] := Subscript[PP, CF]@Module[
{vs=Cases[\[ScriptCapitalE],Subscript[(XX|Y|Z|A|B|b|s|t|a|x|y|z|SuperStar[XX]|SuperStar[Y]|SuperStar[Z]|SuperStar[A]|SuperStar[B]|SuperStar[s]|SuperStar[t]|SuperStar[b]|SuperStar[a]|SuperStar[x]|SuperStar[y]|SuperStar[z]), _],\[Infinity]]\[Union]{XX,Y,Z,A,B,b,s,t,a,x,y,z,SuperStar[XX],SuperStar[Y],SuperStar[Z],SuperStar[A],SuperStar[B],SuperStar[s],SuperStar[t],SuperStar[b],SuperStar[a],SuperStar[x],SuperStar[y],SuperStar[z]}},
Total[CoefficientRules[Expand[\[ScriptCapitalE]], vs] /. (ps_->c_) :> CCF[c](Times@@(vs^ps))]
];


(* ::Input::Initialization:: *)
K\[Delta]/:Subscript[K\[Delta], i_,j_]:=If[i===j,1,0];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]/:\[DoubleStruckCapitalE][L1_,Q1_,P1_]\[Congruent]\[DoubleStruckCapitalE][L2_,Q2_,P2_]:=CF[L1==L2]\[And]CF[Q1==Q2]\[And]CF[Normal[P1-P2]==0];
\[DoubleStruckCapitalE]/:\[DoubleStruckCapitalE][L1_,Q1_,P1_]\[DoubleStruckCapitalE][L2_,Q2_,P2_]:=\[DoubleStruckCapitalE][L1+L2,Q1+Q2,P1*P2];
Subscript[\[DoubleStruckCapitalE][L_,Q_,P_], $k_]:=\[DoubleStruckCapitalE][L,Q,Series[Normal@P,{\[Epsilon],0,$k}]];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]3@Subscript[\[DoubleStruckCapitalE], sp___][\[Omega]_,L_,Q_,P_]:=Module[
{NP=Normal[P]},
Subscript[\[DoubleStruckCapitalE], sp][L,\[Omega]^-1 Q, (\[Omega]^-1 NP /. \[Epsilon]->\[Omega]^-4 \[Epsilon])+O[\[Epsilon]]^($k+1)] // CF
];
\[DoubleStruckCapitalE]4@Subscript[\[DoubleStruckCapitalE], sp___][L_,Q_,P_]:=Module[
{NP=Normal[P],\[Omega]},
\[Omega]=(NP/.\[Epsilon]->0)^-1;
Subscript[\[DoubleStruckCapitalE], sp][\[Omega],L,\[Omega] Q, (\[Omega] NP /. \[Epsilon]->\[Omega]^4 \[Epsilon])+O[\[Epsilon]]^($k+1)] // CF
];


(* ::Input::Initialization:: *)
SuperStar[(Subscript[u_, i_])]:=Subscript[(SuperStar[u]), i];
SuperStar[(SuperStar[(Subscript[u_, i_])])]:=Subscript[u, i];
SuperStar[(Subscript[(SuperStar[(u_)]), i_])]:=Subscript[u, i];
SuperStar[(SuperStar[(u_)])]:=u;


(* ::Input::Initialization:: *)
collect[sd_SeriesData, \[Zeta]_] := MapAt[collect[#,\[Zeta]]&,sd,3];
collect[\[ScriptCapitalE]_,\[Zeta]_] := Subscript[PP, Collect]@Collect[\[ScriptCapitalE],\[Zeta]];
\!\(\*SubscriptBox[\(Zip\), \({}\)]\)[P_]:=P; \!\(\*SubscriptBox[\(Zip\), \({\[Zeta]_, \[Zeta]s___}\)]\)[P_] := Subscript[PP, Zip][
(collect[P//\!\(\*SubscriptBox[\(Zip\), \({\[Zeta]s}\)]\),\[Zeta]] /. f_. \[Zeta]^d_.:>\!\(
\*SubscriptBox[\(\[PartialD]\), \({
\*SuperscriptBox[\(\[Zeta]\), \(*\)], d}\)]f\)) /. SuperStar[\[Zeta]]->0]


(* ::Input::Initialization:: *)
Subscript[QZip, \[Zeta]s_List]@\[DoubleStruckCapitalE][L_,Q_,P_] := Subscript[PP, QZip]@Module[{\[Zeta],z,zs,c,ys,\[Eta]s,qt,zrule,\[Zeta]rule},
zs=Table[SuperStar[\[Zeta]],{\[Zeta],\[Zeta]s}];
c=CF[Q/.Alternatives@@(\[Zeta]s\[Union]zs)->0];
ys=CF@Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(\[Zeta]\)]\((Q /. Alternatives @@ zs -> 0)\)\),{\[Zeta],\[Zeta]s}];
\[Eta]s=CF@Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(z\)]\((Q /. Alternatives @@ \[Zeta]s -> 0)\)\),{z,zs}];
qt=CF@Inverse@Table[Subscript[K\[Delta], z,SuperStar[\[Zeta]]]-\!\(
\*SubscriptBox[\(\[PartialD]\), \(z, \[Zeta]\)]Q\),{\[Zeta],\[Zeta]s},{z,zs}];
zrule=Thread[zs->CF[qt . (zs+ys)]];
\[Zeta]rule=Thread[\[Zeta]s->\[Zeta]s+\[Eta]s . qt];
CF /@ \[DoubleStruckCapitalE][L,c+\[Eta]s . qt . ys,Det[qt]Subscript[Zip, \[Zeta]s][P/.(zrule\[Union]\[Zeta]rule)]] ];


(* ::Input::Initialization:: *)
U2l={\!\(
\*SubsuperscriptBox[\(\[DoubleStruckB]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(\(-p\)\ 
\*SubscriptBox[\(b\), \(i\)]\)]\),\[DoubleStruckB]^p_.->E^(-p b),\!\(
\*SubsuperscriptBox[\(\[DoubleStruckA]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(\(-p\)\ \ 
\*SubscriptBox[\(a\), \(i\)]\)]\),\[DoubleStruckA]^p_.->E^(-p a), \!\(
\*SubsuperscriptBox[\(T\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[\(t\), \(i\)]\)]\),T^p_.->E^(p t),\!\(
\*SubsuperscriptBox[\(S\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[\(s\), \(i\)]\)]\),S^p_.->E^(p s),\!\(
\*SubsuperscriptBox[\(\[ScriptA]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[
SuperscriptBox[\(a\), \(*\)], \(i\)]\)]\),\[ScriptA]^p_.->E^(p SuperStar[a]),\!\(
\*SubsuperscriptBox[\(\[ScriptB]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[
SuperscriptBox[\(b\), \(*\)], \(i\)]\)]\),\[ScriptB]^p_.->E^(p SuperStar[b]),\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(\(-p\)\ 
\*SubscriptBox[\(B\), \(i\)]\)]\),\[DoubleStruckCapitalB]^p_.->E^(-p B),\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(\(-p\)\ 
\*SubscriptBox[\(A\), \(i\)]\)]\),\[DoubleStruckCapitalA]^p_.->E^(-p A),\!\(
\*SubsuperscriptBox[\(\[ScriptCapitalA]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[
SuperscriptBox[\(A\), \(*\)], \(i\)]\)]\),\[ScriptCapitalA]^p_.->E^(p SuperStar[A]),\!\(
\*SubsuperscriptBox[\(\[ScriptCapitalB]\), \(i_\), \(p_.\)] -> 
\*SuperscriptBox[\(E\), \(p\ 
\*SubscriptBox[
SuperscriptBox[\(B\), \(*\)], \(i\)]\)]\),\[ScriptCapitalB]^p_.->E^(p SuperStar[B])}; 
l2U={E^(c_. Subscript[b, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[DoubleStruckB]\), \(i\), \(-c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. b+d_.):>\[DoubleStruckB]^-c E^d,E^(c_. Subscript[a, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[DoubleStruckA]\), \(i\), \(-c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. a+d_.):>\[DoubleStruckA]^-c E^d,
E^(c_. Subscript[t, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(T\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. t+d_.):>T^c E^d,E^(c_. Subscript[s, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(S\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. s+d_.):>S^c E^d,
E^(c_. Subscript[SuperStar[a], i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[ScriptA]\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. SuperStar[a]+d_.):>\[ScriptA]^c E^d,E^(c_. Subscript[SuperStar[b], i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[ScriptB]\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. SuperStar[b]+d_.):>\[ScriptB]^c E^d,E^(c_. Subscript[B, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(-c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. B+d_.):>\[DoubleStruckCapitalB]^-c E^d,E^(c_. Subscript[A, i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(-c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. A+d_.):>\[DoubleStruckCapitalA]^-c E^d,
E^(c_. Subscript[SuperStar[A], i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[ScriptCapitalA]\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. SuperStar[A]+d_.):>\[ScriptCapitalA]^c E^d,E^(c_. Subscript[SuperStar[B], i_]+d_.):>\!\(
\*SubsuperscriptBox[\(\[ScriptCapitalB]\), \(i\), \(c\)] 
\*SuperscriptBox[\(E\), \(d\)]\),E^(c_. SuperStar[B]+d_.):>\[ScriptCapitalB]^c E^d,
E^\[ScriptCapitalE]_:>E^Expand@\[ScriptCapitalE]}; 


(* ::Input::Initialization:: *)
Subscript[LZip, \[Zeta]s_List]@\[DoubleStruckCapitalE][L_,Q_,P_] := Subscript[PP, LZip]@Module[{\[Zeta],z,zs,c,ys,\[Eta]s,lt,zrule,Zrule,\[Zeta]rule,Q1,EEQ,EQ},
zs=Table[SuperStar[\[Zeta]],{\[Zeta],\[Zeta]s}];
c=L/.Alternatives@@(\[Zeta]s\[Union]zs)->0;
ys=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(\[Zeta]\)]\((L /. Alternatives @@ zs -> 0)\)\),{\[Zeta],\[Zeta]s}];
\[Eta]s=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(z\)]\((L /. Alternatives @@ \[Zeta]s -> 0)\)\),{z,zs}];
lt=Inverse@Table[Subscript[K\[Delta], z,SuperStar[\[Zeta]]]-\!\(
\*SubscriptBox[\(\[PartialD]\), \(z, \[Zeta]\)]L\),{\[Zeta],\[Zeta]s},{z,zs}];
zrule=Thread[zs->lt . (zs+ys)];
\[Zeta]rule=Thread[\[Zeta]s->\[Zeta]s+\[Eta]s . lt];
Q1=Q/.U2l/.(zrule\[Union]\[Zeta]rule);
EEQ[ps___]:=EEQ[ps]=\!\(\*SubscriptBox[\(PP\), \("\<EEQ\>"\)]\)@(CF[E^-Q1 D[E^Q1,Sequence@@Thread[{zs,{ps}}]]]/.Alternatives@@zs->0//.l2U);
CF /@ ((*CF/@*)\[DoubleStruckCapitalE][
c+\[Eta]s . lt . ys,Q1/.Alternatives@@zs->0,
Det[lt](Subscript[Zip, \[Zeta]s][(EQ@@zs)(P/.U2l/.(zrule\[Union]\[Zeta]rule))] /. \!\(\*
TagBox[
StyleBox[
RowBox[{
RowBox[{
RowBox[{"Derivative", "[", "ps___", "]"}], "[", "EQ", "]"}], "[", "___", "]"}],
ShowSpecialCharacters->False,
ShowStringCharacters->True,
NumberMarks->True],
FullForm]\) :> EEQ[ps] /. _EQ->1)
]//.l2U)
 ];


(* ::Input::Initialization:: *)
\!\(\*SubscriptBox[\(B\), \({}\)]\)[L_,R_]:=L R;
\!\(\*SubscriptBox[\(B\), \({is__}\)]\)[L_\[DoubleStruckCapitalE],R_\[DoubleStruckCapitalE]] := Subscript[PP, Bind]@Module[{n},
Times[
L/.Table[Subscript[(v:XX|Y|Z|A|\[DoubleStruckCapitalA]|B|\[DoubleStruckCapitalB]|s|t|S|T|b|(*\[DoubleStruckB]|*)a(*|\[DoubleStruckA]*)|x|y|z), i]->Subscript[v, n@i],{i,{is}}],
R/.Table[Subscript[(v:SuperStar[XX]|SuperStar[Y]|SuperStar[Z]|SuperStar[A](*|\[ScriptCapitalA]*)|SuperStar[B]|(*\[ScriptCapitalB]| *)SuperStar[b]|SuperStar[s]|SuperStar[t]|SuperStar[a]|\[ScriptA]|\[ScriptB]|SuperStar[x]|SuperStar[y]|SuperStar[z]), i]->Subscript[v, n@i],{i,{is}}]
] // Subscript[LZip, Flatten@Table[{Subscript[SuperStar[A], n@i],Subscript[SuperStar[B], n@i],Subscript[(SuperStar[s]), n@i],Subscript[(SuperStar[t]), n@i],Subscript[b, n@i],Subscript[a, n@i]},{i,{is}}]] // Subscript[QZip, Flatten@Table[{Subscript[XX, n@i],Subscript[SuperStar[Y], n@i],Subscript[y, n@i],Subscript[SuperStar[x], n@i]},{i,{is}}]]//Subscript[QZip, Flatten@Table[{Subscript[SuperStar[Z], n@i],Subscript[z, n@i]},{i,{is}}]]];
Subscript[B, is___][L_,R_]:=\!\(\*SubscriptBox[\(B\), \({is}\)]\)[L,R];


(* ::Input::Initialization:: *)
\!\(\*SubscriptBox[\(STB\), \({}\)]\)[L_,R_]:=L R;
\!\(\*SubscriptBox[\(STB\), \({is__}\)]\)[L_\[DoubleStruckCapitalE],R_\[DoubleStruckCapitalE]] := Subscript[PP, STBind]@Module[{n},
Times[
L/.Table[Subscript[(v:XX|Y|Z|b|\[DoubleStruckB]|a|\[DoubleStruckA]|x|y|z), i]->Subscript[v, n@i],{i,{is}}],
R/.Table[Subscript[(v:SuperStar[XX]|SuperStar[Y]|SuperStar[Z]| SuperStar[b]|SuperStar[a]|\[ScriptA]|\[ScriptB]|SuperStar[x]|SuperStar[y]|SuperStar[z]), i]->Subscript[v, n@i],{i,{is}}]
] // Subscript[LZip, Flatten@Table[{Subscript[b, n@i],Subscript[a, n@i]},{i,{is}}]] // Subscript[QZip, Flatten@Table[{Subscript[XX, n@i],Subscript[SuperStar[Y], n@i],Subscript[y, n@i],Subscript[SuperStar[x], n@i]},{i,{is}}]]//Subscript[QZip, Flatten@Table[{Subscript[SuperStar[Z], n@i],Subscript[z, n@i]},{i,{is}}]]];
Subscript[STB, is___][L_,R_]:=\!\(\*SubscriptBox[\(STB\), \({is}\)]\)[L,R];


(* ::Input::Initialization:: *)
Subscript[B, is_List][Subscript[\[DoubleStruckCapitalE], d1_->r1_][L1_,Q1_,P1_],Subscript[\[DoubleStruckCapitalE], d2_->r2_][L2_,Q2_,P2_]]:=Subscript[\[DoubleStruckCapitalE], (d1\[Union]Complement[d2,is])->(r2\[Union]Complement[r1,is])]@@Subscript[B, is][\[DoubleStruckCapitalE][L1,Q1,P1],\[DoubleStruckCapitalE][L2,Q2,P2]];
Subscript[STB, is_List][Subscript[\[DoubleStruckCapitalE], d1_->r1_][L1_,Q1_,P1_],Subscript[\[DoubleStruckCapitalE], d2_->r2_][L2_,Q2_,P2_]]:=Subscript[\[DoubleStruckCapitalE], (d1\[Union]Complement[d2,is])->(r2\[Union]Complement[r1,is])]@@Subscript[STB, is][\[DoubleStruckCapitalE][L1,Q1,P1],\[DoubleStruckCapitalE][L2,Q2,P2]];
Subscript[\[DoubleStruckCapitalE], d1_->r1_][L1_,Q1_,P1_]//Subscript[\[DoubleStruckCapitalE], d2_->r2_][L2_,Q2_,P2_] := Subscript[B, r1\[Intersection]d2][Subscript[\[DoubleStruckCapitalE], d1->r1][L1,Q1,P1],Subscript[\[DoubleStruckCapitalE], d2->r2][L2,Q2,P2]];
Subscript[\[DoubleStruckCapitalE], d1_->r1_][L1_,Q1_,P1_]\[Congruent]Subscript[\[DoubleStruckCapitalE], d2_->r2_][L2_,Q2_,P2_] ^:= (d1==d2)\[And](r1==r2)\[And](\[DoubleStruckCapitalE][L1,Q1,P1]\[Congruent]\[DoubleStruckCapitalE][L2,Q2,P2]);
Subscript[\[DoubleStruckCapitalE], d1_->r1_][L1_,Q1_,P1_]Subscript[\[DoubleStruckCapitalE], d2_->r2_][L2_,Q2_,P2_] ^:= Subscript[\[DoubleStruckCapitalE], (d1\[Union]d2)->(r1\[Union]r2)]@@(\[DoubleStruckCapitalE][L1,Q1,P1]\[DoubleStruckCapitalE][L2,Q2,P2]);
Subscript[Subscript[\[DoubleStruckCapitalE], d_->r_][L_,Q_,P_], $k_]:=Subscript[\[DoubleStruckCapitalE], d->r]@@Subscript[\[DoubleStruckCapitalE][L,Q,P], $k];
Subscript[\[DoubleStruckCapitalE], _][\[ScriptCapitalE]___][i_]:={\[ScriptCapitalE]}[[i]];



(* ::Input::Initialization:: *)
SetAttributes[Define, HoldAll];
Define[def_,defs__] := (Define[def]; Define[defs];);
Define[Subscript[op_, is__]=\[ScriptCapitalE]_] := Module[{SD,ii,jj,kk,isp,nis,nisp,sis},Block[{i,j,k},
ReleaseHold[Hold[
SD[Subscript[op, nisp,$k_Integer],Subscript[PP, Boot]@Block[{i,j,k},Subscript[op, isp,$k]=\[ScriptCapitalE];Subscript[op, nis,$k]]];
SD[Subscript[op, isp],\!\(\*SubscriptBox[\(op\), \({is}, $k\)]\)]; SD[Subscript[op, sis__],\!\(\*SubscriptBox[\(op\), \({sis}\)]\)];
]/. {SD->SetDelayed,
isp->{is}/.{i->i_,j->j_,k->k_},
nis->{is}/.{i->ii,j->jj,k->kk},
nisp->{is}/.{i->ii_,j->jj_,k->kk_}
}]  ]]


(* ::Input::Initialization:: *)
$k=1; 


(* ::Input::Initialization:: *)
Define[Subscript[am, i,j->k]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[(Subscript[SuperStar[a], i]+Subscript[SuperStar[a], j])Subscript[a, k]+(Subscript[SuperStar[b], i]+Subscript[SuperStar[b], j])Subscript[b, k],(E^(Subscript[(SuperStar[b]), j]+Subscript[(SuperStar[a]), j]) Subscript[SuperStar[z], i]+Subscript[SuperStar[z], j]+E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[SuperStar[x], i] Subscript[(SuperStar[y]), j])Subscript[z, k]+(E^(-Subscript[(SuperStar[a]), j]+2Subscript[(SuperStar[b]), j]) Subscript[SuperStar[y], i]+Subscript[SuperStar[y], j])Subscript[y, k]+(E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[SuperStar[x], i]+Subscript[SuperStar[x], j])Subscript[x, k],1+\[Epsilon](\[HBar] Subscript[(SuperStar[z]), j] Subscript[(SuperStar[x]), i] E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[z, k] Subscript[x, k]+\[HBar] Subscript[(SuperStar[z]), j] Subscript[(SuperStar[x]), i] Subscript[(SuperStar[y]), j] E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[z, k] Subscript[z, k]-\[HBar] Subscript[(SuperStar[z]), j] Subscript[(SuperStar[y]), i] E^(2Subscript[(SuperStar[b]), j]-Subscript[(SuperStar[a]), j]) Subscript[z, k] Subscript[y, k]-\[HBar] Subscript[(SuperStar[y]), i] Subscript[(SuperStar[x]), i] Subscript[(SuperStar[y]), j] E^(Subscript[(SuperStar[a]), j]+Subscript[(SuperStar[b]), j]) Subscript[z, k] Subscript[y, k]-\[HBar] Subscript[(SuperStar[x]), i] E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[(SuperStar[y]), j] Subscript[(SuperStar[y]), j] Subscript[z, k] Subscript[y, k]-\[HBar] Subscript[(SuperStar[x]), i] E^(-Subscript[(SuperStar[b]), j]+2Subscript[(SuperStar[a]), j]) Subscript[(SuperStar[y]), j] Subscript[y, k] Subscript[x, k])+O[\[Epsilon]]^2], $k],
Subscript[bm, i,j->k]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[Subscript[A, k] Subscript[SuperStar[A], i]+Subscript[A, k] Subscript[SuperStar[A], j]+Subscript[B, k] Subscript[SuperStar[B], i]+Subscript[B, k] Subscript[SuperStar[B], j],Subscript[XX, k] Subscript[SuperStar[XX], i]+Subscript[XX, k] Subscript[SuperStar[XX], j]+Subscript[Y, k] Subscript[SuperStar[Y], i]+Subscript[Y, k] Subscript[SuperStar[Y], j]+Subscript[Z, k] Subscript[SuperStar[Z], i]+Subscript[Z, k] Subscript[SuperStar[Z], j],1+(-Subscript[XX, k] Subscript[(SuperStar[A]), i] Subscript[(SuperStar[XX]), j]+\[HBar] Subscript[XX, k] Subscript[Y, k] Subscript[(SuperStar[XX]), j] Subscript[(SuperStar[Y]), i]-Subscript[Y, k] Subscript[(SuperStar[B]), i] Subscript[(SuperStar[Y]), j]+2Subscript[Z, k] Subscript[(SuperStar[XX]), i] Subscript[(SuperStar[Y]), j]-\[HBar] Subscript[XX, k] Subscript[Z, k] Subscript[(SuperStar[XX]), j] Subscript[(SuperStar[Z]), i]+\[HBar] Subscript[Y, k] Subscript[Z, k] Subscript[(SuperStar[Y]), j] Subscript[(SuperStar[Z]), i]-Subscript[Z, k] Subscript[(SuperStar[A]), i] Subscript[(SuperStar[Z]), j]-Subscript[Z, k] Subscript[(SuperStar[B]), i] Subscript[(SuperStar[Z]), j])\[Epsilon]+O[\[Epsilon]]^2], $k]];


(* ::Input::Initialization:: *)
Define[Subscript[R, i,j]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[\[HBar] Subscript[A, i] Subscript[a, j]+\[HBar] Subscript[B, i] Subscript[b, j],\[HBar] Subscript[XX, i] Subscript[x, j]+\[HBar] Subscript[Y, i] Subscript[y, j]+\[HBar] Subscript[Z, i] Subscript[z, j],E^(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 2\), \($k + 1\)]\ 
\*FractionBox[\(
\*SuperscriptBox[\((
\*SuperscriptBox[\(E\), \(\(-2\) \[Epsilon]\ \[HBar]\)] - 1)\), \(k\)] 
\*SuperscriptBox[\((\[HBar]\ 
\*SubscriptBox[\(XX\), \(i\)] 
\*SubscriptBox[\(x\), \(j\)])\), \(k\)]\), \(k \((1 - 
\*SuperscriptBox[\(E\), \(\(-2\) k\ \[Epsilon]\ \[HBar]\)])\)\)]\))E^(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(l = 2\), \($k + 1\)]\ 
\*FractionBox[\(
\*SuperscriptBox[\((
\*SuperscriptBox[\(E\), \(\(-2\) \[Epsilon]\ \[HBar]\)] - 1)\), \(l\)] 
\*SuperscriptBox[\((\[HBar]\ 
\*SubscriptBox[\(Y\), \(i\)] 
\*SubscriptBox[\(y\), \(j\)])\), \(l\)]\), \(l \((1 - 
\*SuperscriptBox[\(E\), \(\(-2\) l\ \[Epsilon]\ \[HBar]\)])\)\)]\))E^(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 2\), \($k + 1\)]\ 
\*FractionBox[\(
\*SuperscriptBox[\((
\*SuperscriptBox[\(E\), \(\(-2\) \[Epsilon]\ \[HBar]\)] - 1)\), \(m\)] 
\*SuperscriptBox[\((\[HBar]\ 
\*SubscriptBox[\(Z\), \(i\)] 
\*SubscriptBox[\(z\), \(j\)])\), \(m\)]\), \(m \((1 - 
\*SuperscriptBox[\(E\), \(\(-2\) m\ \[Epsilon]\ \[HBar]\)])\)\)]\))], $k],
Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[-\[HBar] Subscript[a, j] Subscript[A, i]-\[HBar] Subscript[b, j] Subscript[B, i],-\[HBar] Subscript[x, j] Subscript[XX, i] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(2\ \[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(-\[HBar]\)]\)+\[HBar]^2 Subscript[XX, i] Subscript[Y, i] Subscript[z, j] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\)-\[HBar] Subscript[z, j] Subscript[Z, i] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\)-\[HBar] Subscript[y, j] Subscript[Y, i] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(-\[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(2\ \[HBar]\)]\),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] {}\)]\)[1/\[HBar] Subscript[SuperStar[A], i] Subscript[SuperStar[a], j]+1/\[HBar] Subscript[SuperStar[B], i] Subscript[(SuperStar[b]), j],1/\[HBar] Subscript[SuperStar[XX], i] Subscript[SuperStar[x], j]+1/\[HBar] Subscript[SuperStar[Y], i] Subscript[SuperStar[y], j]+1/\[HBar] Subscript[SuperStar[Z], i] Subscript[SuperStar[z], j],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, j]=Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]~Subscript[B, i]~Subscript[P, i,j],
Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[-Subscript[SuperStar[a], i] Subscript[a, i]-Subscript[SuperStar[b], i] Subscript[b, i],-E^(-Subscript[(SuperStar[b]), i]-Subscript[(SuperStar[a]), i]) Subscript[SuperStar[z], i] Subscript[z, i]+E^(-Subscript[(SuperStar[b]), i]-Subscript[(SuperStar[a]), i]) Subscript[SuperStar[y], i] Subscript[(SuperStar[x]), i] Subscript[z, i]-E^(-2 Subscript[(SuperStar[b]), i]+Subscript[(SuperStar[a]), i]) Subscript[SuperStar[y], i] Subscript[y, i]-E^(Subscript[(SuperStar[b]), i]-2Subscript[(SuperStar[a]), i]) Subscript[SuperStar[x], i] Subscript[x, i],1+If[$k==0, 0,Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, $k - 1\)]\)), $k][3]-
(Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, 0\)]\)), $k]~Subscript[B, i]~Subscript[aS, i]~Subscript[B, i]~Subscript[(\!\(\*SubscriptBox[
OverscriptBox[\(aS\), \(_\)], \({i}, $k - 1\)]\)), $k])[3]]]]


(* ::Input::Initialization:: *)
Define[Subscript[bS, i]=Subscript[R, i,1]~Subscript[B, 1]~Subscript[aS, 1]~Subscript[B, 1]~Subscript[P, i,1],
Subscript[\!\(\*OverscriptBox[\(bS\), \(_\)]\), i]=Subscript[R, i,1]~Subscript[B, 1]~Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 1]~Subscript[B, 1]~Subscript[P, i,1],
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]=(\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {i, j}\)]\)[Subscript[(SuperStar[A]), i] Subscript[A, i]+Subscript[(SuperStar[B]), i] Subscript[B, i]+Subscript[SuperStar[b], j] Subscript[b, j] + Subscript[SuperStar[a], j] Subscript[a, j],Subscript[SuperStar[y], j] Subscript[y, j]+ Subscript[SuperStar[x], j] Subscript[x, j] + Subscript[SuperStar[z], j] Subscript[z, j] +Subscript[(SuperStar[XX]), i] Subscript[XX, i]+Subscript[(SuperStar[Y]), i] Subscript[Y, i]+Subscript[SuperStar[Z], i] Subscript[Z, i],1](Subscript[a\[CapitalDelta], i->1,2]//Subscript[a\[CapitalDelta], 2->2,3]//Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 3])(Subscript[b\[CapitalDelta], j->-1,-2]//Subscript[b\[CapitalDelta], -2->-2,-3]))//(Subscript[P, -1,3] Subscript[P, -3,1] Subscript[am, 2,j->k] Subscript[bm, i,-2->k]),
Subscript[dS, i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {1, 2}\)]\)[Subscript[(SuperStar[A]), i] Subscript[A, 1]+Subscript[(SuperStar[B]), i] Subscript[B, 1]+Subscript[SuperStar[b], i] Subscript[b, 2] + Subscript[SuperStar[a], i] Subscript[a, 2],Subscript[SuperStar[y], i] Subscript[y, 2]+ Subscript[SuperStar[x], i] Subscript[x, 2] + Subscript[SuperStar[z], i] Subscript[z, 2] +Subscript[(SuperStar[XX]), i] Subscript[XX, 1]+Subscript[(SuperStar[Y]), i] Subscript[Y, 1]+Subscript[SuperStar[Z], i] Subscript[Z, 1],1]//(Subscript[\!\(\*OverscriptBox[\(bS\), \(_\)]\), 1] Subscript[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]),
Subscript[\!\(\*OverscriptBox[\(dS\), \(_\)]\), i]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {1, 2}\)]\)[Subscript[(SuperStar[A]), i] Subscript[A, 1]+Subscript[(SuperStar[B]), i] Subscript[B, 1]+Subscript[SuperStar[b], i] Subscript[b, 2] + Subscript[SuperStar[a], i] Subscript[a, 2],Subscript[SuperStar[y], i] Subscript[y, 2]+ Subscript[SuperStar[x], i] Subscript[x, 2] + Subscript[SuperStar[z], i] Subscript[z, 2] +Subscript[(SuperStar[XX]), i] Subscript[XX, 1]+Subscript[(SuperStar[Y]), i] Subscript[Y, 1]+Subscript[SuperStar[Z], i] Subscript[Z, 1],1]//(Subscript[bS, 1] Subscript[\!\(\*OverscriptBox[\(aS\), \(_\)]\), 2])//Subscript[dm, 2,1->i]]


(* ::Input::Initialization:: *)
Define[Subscript[C, i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0,0,1/(\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\ 
\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\))-(\[HBar](Subscript[a, i]+Subscript[b, i]) \[Epsilon])/(\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\ 
\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\))+O[\[Epsilon]]^2], $k],
Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0,0,(\!\(
\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\ 
\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\)+(\[HBar] Subscript[a, i] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\)+\[HBar] Subscript[b, i] \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalA]\), \(i\), \(\[HBar]\)]\) \!\(\*SubsuperscriptBox[\(\[DoubleStruckCapitalB]\), \(i\), \(\[HBar]\)]\)) \[Epsilon])+O[\[Epsilon]]^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[AB2st, i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[Subscript[SuperStar[b], i] Subscript[b, i] + Subscript[SuperStar[a], i] Subscript[a, i]+Subscript[(SuperStar[A]), i](2/3 (Subscript[s, i]+Subscript[t, i]/2))+Subscript[(SuperStar[B]), i](2/3 (Subscript[t, i]+Subscript[s, i]/2)),Subscript[(SuperStar[XX]), i] Subscript[XX, i]+Subscript[(SuperStar[Y]), i] Subscript[Y, i]+Subscript[SuperStar[Z], i] Subscript[Z, i]+Subscript[SuperStar[y], i] Subscript[y, i]+Subscript[SuperStar[x], i] Subscript[x, i]+Subscript[SuperStar[z], i] Subscript[z, i],1-\[Epsilon] Subscript[(SuperStar[A]), i] 1/3 (2Subscript[a, i]+Subscript[b, i])-\[Epsilon] Subscript[(SuperStar[B]), i] 1/3 (2Subscript[b, i]+Subscript[a, i])+O[\[Epsilon]]^2], $k],
Subscript[st2AB, i]=Subscript[\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i} \[Rule] {i}\)]\)[Subscript[SuperStar[b], i] Subscript[b, i] + Subscript[SuperStar[a], i] Subscript[a, i]+Subscript[(SuperStar[s]), i](2Subscript[A, i]-Subscript[B, i])+Subscript[(SuperStar[t]), i](2Subscript[B, i]-Subscript[A, i]),Subscript[(SuperStar[XX]), i] Subscript[XX, i]+Subscript[(SuperStar[Y]), i] Subscript[Y, i]+Subscript[SuperStar[Z], i] Subscript[Z, i]+Subscript[SuperStar[y], i] Subscript[y, i]+Subscript[SuperStar[x], i] Subscript[x, i]+Subscript[SuperStar[z], i] Subscript[z, i],1+\[Epsilon] Subscript[(SuperStar[s]), i] Subscript[a, i]+\[Epsilon] Subscript[(SuperStar[t]), i] Subscript[b, i]+O[\[Epsilon]]^2], $k]]


(* ::Input::Initialization:: *)
Define[Subscript[stR, i,j]=(Subscript[R, i,j]~\!\(\*SubscriptBox[\(B\), \({i, j}\)]\)~(Subscript[AB2st, i] Subscript[AB2st, j]))//Simplify,
Subscript[\!\(\*OverscriptBox[\(stR\), \(_\)]\), i,j]=(Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]~\!\(\*SubscriptBox[\(B\), \({i, j}\)]\)~(Subscript[AB2st, i] Subscript[AB2st, j]))//Simplify,
Subscript[\!\(\*OverscriptBox[\(stC\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))//Simplify,
Subscript[stC, i]=(Subscript[C, i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))//Simplify,
Subscript[\!\(\*OverscriptBox[\(stKink\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(Kink\), \(_\)]\), i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))//Simplify,
Subscript[stKink, i]=(Subscript[Kink, i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))//Simplify,
Subscript[stdm, i,j->k]=((Subscript[st2AB, i] Subscript[st2AB, j])~Subscript[B, i,j]~Subscript[dm, i,j->k]~Subscript[B, k]~Subscript[AB2st, k]),
Subscript[std\[CapitalDelta], i->j,k]=(Subscript[st2AB, i]//Subscript[d\[CapitalDelta], i->j,k]//(Subscript[AB2st, j] Subscript[AB2st, k])),
Subscript[stdS, i]=(Subscript[st2AB, i]//Subscript[dS, i]//Subscript[AB2st, i]),
Subscript[stP, i,j]=((Subscript[st2AB, i] Subscript[st2AB, j])//Subscript[P, i,j]),
Subscript[dd\[CapitalDelta], i->j,k]=(Subscript[st2AB, i]//Subscript[d\[CapitalDelta], i->j,k]//(Subscript[AB2st, j] Subscript[AB2st, k]))/.{Subscript[S, j|k]->S,Subscript[T, j|k]->T,Subscript[t, j|k]->t,Subscript[s, j|k]->s,Subscript[(SuperStar[s]), i]->0,Subscript[(SuperStar[t]), i]->0},
Subscript[ddS, i]=(Subscript[st2AB, i]//Subscript[dS, i]//Subscript[AB2st, i])/.{Subscript[S, i]->S,Subscript[T, i]->T,Subscript[s, i]->s,Subscript[t, i]->t,Subscript[(SuperStar[s]), i]->0,Subscript[(SuperStar[t]), i]->0},
Subscript[PP, i,j]=((Subscript[st2AB, i] Subscript[st2AB, j])//Subscript[P, i,j])/.{Subscript[(SuperStar[s]), i|j]->0,Subscript[(SuperStar[t]), i|j]->0},
Subscript[RR, i,j]=(Subscript[R, i,j]//(Subscript[AB2st, i] Subscript[AB2st, j]))/.{Subscript[t, i|j]->t,Subscript[s, i|j]->s},
Subscript[\!\(\*OverscriptBox[\(RR\), \(_\)]\), i,j]=(Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i,j]//(Subscript[AB2st, i] Subscript[AB2st, j]))/.{Subscript[t, i|j]->t,Subscript[s, i|j]->s,Subscript[S, i|j]->S,Subscript[T, i|j]->T},
Subscript[\!\(\*OverscriptBox[\(CC\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))/.{Subscript[S, i|j]->S,Subscript[T, i|j]->T}//Simplify,
Subscript[CC, i]=(Subscript[C, i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))/.{Subscript[S, i|j]->S,Subscript[T, i|j]->T}//Simplify,
Subscript[\!\(\*OverscriptBox[\(KKink\), \(_\)]\), i]=(Subscript[\!\(\*OverscriptBox[\(Kink\), \(_\)]\), i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))/.{Subscript[t, i|j]->t,Subscript[s, i|j]->s,Subscript[S, i|j]->S,Subscript[T, i|j]->T}//Simplify,
Subscript[KKink, i]=(Subscript[Kink, i]~\!\(\*SubscriptBox[\(B\), \({i}\)]\)~(Subscript[AB2st, i]))/.{Subscript[t, i|j]->t,Subscript[s, i|j]->s,Subscript[S, i|j]->S,Subscript[T, i|j]->T}//Simplify,
Subscript[ddm, i,j->k]=((Subscript[st2AB, i] Subscript[st2AB, j])//Subscript[dm, i,j->k]//Subscript[AB2st, k])/.{Subscript[S, k]->S,Subscript[T, k]->T,Subscript[t, k]->t,Subscript[s, k]->s,Subscript[(SuperStar[s]), i|j]->0,Subscript[(SuperStar[t]), i|j]->0}];



