(* ::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:: *)
SetDirectory["C:\\drorbn\\AcademicPensieve\\Talks\\Bonn-2505"];
Once[<<KnotTheory`; <<Rot.m];


(* ::Input::Initialization:: *)
CF[\[Omega]_. \[ScriptCapitalE]_\[DoubleStruckCapitalE]]:=CF[\[Omega]]CF/@\[ScriptCapitalE];
CF[\[ScriptCapitalE]_List]:=CF/@\[ScriptCapitalE];
CF[\[ScriptCapitalE]_] := Module[{vs,ps,c},
vs=Cases[\[ScriptCapitalE],Subscript[(x|p|\[Xi]|\[Pi]|g), __],\[Infinity]]\[Union]{\[Epsilon]};
Total[CoefficientRules[Expand[\[ScriptCapitalE]], vs] /. (ps_->c_) :> Factor[c](Times@@(vs^ps))] ];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]/:\[DoubleStruckCapitalE][A_]\[DoubleStruckCapitalE][B_]:=\[DoubleStruckCapitalE][A+B];


(* ::Input::Initialization:: *)
$\[Pi]=Identity; (* The Wisdom Projection *)


(* ::Input::Initialization:: *)
Unprotect[Integrate];
\[Integral]\[Omega]_. \[DoubleStruckCapitalE][L_]\[DifferentialD](vs_List):=Module[{n,L0,Q,\[CapitalDelta],G,Z0,Z,\[Lambda],DZ,DDZ,FZ,a,b},
n=Length@vs; L0=L/.\[Epsilon]->0;
Q=Table[(-\!\(
\*SubscriptBox[\(\[PartialD]\), \(vs[[\(a\)\(]\)], vs[[\(b\)\(]\)]\)]L0\))/.Thread[vs->0]/.Subscript[(p|x), __]->0,{a,n},{b,n}];
If[(\[CapitalDelta]=Det[Q])==0,Return@"\!\(\*
StyleBox[\"Degenerate\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"Q\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"!\",\nFontColor->RGBColor[1, 0, 0]]\)"];
Z=Z0=CF@$\[Pi][L+vs . Q . vs/2]; G=Inverse[Q];
FixedPoint[(DZ=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(v\)]Z\),{v,vs}];
DDZ=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(u\)]DZ\),{u,vs}];
FZ=Sum[G[[a,b]](DDZ[[a,b]]+DZ[[a]]DZ[[b]]),{a,n},{b,n}]/2;
Z=CF[Z0+\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\($\[Pi][FZ]\ \[DifferentialD]\[Lambda]\)\)])&,Z];
PowerExpand@Factor[\[Omega] \[CapitalDelta]^(-1/2)]\[DoubleStruckCapitalE][CF[Z/.\[Lambda]->1/.Thread[vs->0]]]];
Protect[Integrate];


(* ::Input::Initialization:: *)
Subscript[T, 3]=Subscript[T, 1] Subscript[T, 2];  SuperPlus[i_]:=i+1;
$\[Pi]=(CF@Normal[#+O[\[Epsilon]]^2]/. {Subscript[\[Pi], is__]:>B^-1 Subscript[\[Pi], is],Subscript[x, is__]:>B^-1 Subscript[x, is],Subscript[p, is__]:>B Subscript[p, is]}/.\[Epsilon] B^b_/;b<0->0/.B->1)&;


(* ::Input::Initialization:: *)
Subscript[vs, i_]:=Sequence[Subscript[p, 1,i],Subscript[p, 2,i],Subscript[p, 3,i],Subscript[x, 1,i],Subscript[x, 2,i],Subscript[x, 3,i]];
\[ScriptCapitalF][is__]:=\[DoubleStruckCapitalE][Sum[Subscript[\[Pi], \[Nu],i] Subscript[p, \[Nu],i],{i,{is}}, {\[Nu],3}]];
\[ScriptCapitalL][K_]:=CF[\[ScriptCapitalL]/@Features[K][[2]]];
vs[K_] := Union@@Table[{Subscript[vs, i]},{i,Features[K][[1]]}]


(* ::Input::Initialization:: *)
\[ScriptCapitalL][Subscript[X, i_,j_][s_]]:=\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] \(\[DoubleStruckCapitalE][CF@Plus[\[IndentingNewLine]
\*SubsuperscriptBox[\(\[Sum]\), \(\[Nu] = 1\), \(3\)]\((
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]i\)])\) + 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]j\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]j\)])\) + \((
\*SubsuperscriptBox[\(T\), \(\[Nu]\), \(s\)] - 1)\) 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)])\))\), \[IndentingNewLine]\((
\*SubsuperscriptBox[\(T\), \(1\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] \((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)])\), \[IndentingNewLine]\[Epsilon]\ s \((
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] \((
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)])\) 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)]/\((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 1)\), \[IndentingNewLine]\[Epsilon]\ s \((1/2 + 
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] - 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - \((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + \((
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + 2\ 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)] - 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)] - 
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)] + \((\((
\*SubsuperscriptBox[\(T\), \(1\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] \((
\*SubsuperscriptBox[\(T\), \(2\), \(2  s\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] - \((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] + 1)\) \((
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + 
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)])\) + \((
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] - 1)\) 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] \((1 - 
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] + 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] + \((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 2)\) 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)])\))\)/\((
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 1)\))\)]]\)\)


(* ::Input::Initialization:: *)
\[ScriptCapitalL][Subscript[C, i_][\[CurlyPhi]_]]:=\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(\[CurlyPhi]\)] \(\[DoubleStruckCapitalE][
\*SubsuperscriptBox[\(\[Sum]\), \(\[Nu] = 1\), \(3\)]
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]i\)])\) + \[Epsilon]\ \[CurlyPhi] \((
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - 1/2)\)]\)\)



