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Copy pathTensorBases.m
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TensorBases.m
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(* ::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. *)
(************************************************************************)
Print["Mathematica package \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)loaded
\!\(\*
StyleBox[\"Authors\",\nFontWeight->\"Bold\"]\): Andreas Gei\[SZ]el, Franz Richard Sattler
\!\(\*
StyleBox[\"Version\",\nFontWeight->\"Bold\"]\): 1.0
\!\(\*
StyleBox[\"Year\",\nFontWeight->\"Bold\"]\): 2024
For a list of available bases, call \!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[]. For further information on a particular basis, call \!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"\!\(\*
StyleBox[\"BasisName\",\nFontColor->GrayLevel[0.5]]\)\"].
This package provides the methods \!\(\*
StyleBox[\"TBGetBasisElement\",\nFontColor->RGBColor[1, 0.5, 0]]\), \!\(\*
StyleBox[\"TBGetInnerProduct\",\nFontColor->RGBColor[1, 0.5, 0]]\), \!\(\*
StyleBox[\"TBGetMetric\",\nFontColor->RGBColor[1, 0.5, 0]]\), \!\(\*
StyleBox[\"TBGetInverseMetric\",\nFontColor->RGBColor[1, 0.5, 0]]\), \!\(\*
StyleBox[\"TBGetProjector\",\nFontColor->RGBColor[1, 0.5, 0]]\) for every tensor basis available.
For closer explanations, please call their usage messages, e.g. \!\(\*
StyleBox[\"TBGetProjector\",\nFontColor->RGBColor[1, 0.5, 0]]\)::\!\(\*
StyleBox[\"usage\",\nFontColor->RGBColor[0, 0, 1]]\).
To build or manipulate bases, please call \!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"BaseBuilder\"].
"]
FormTracerLoaded[]:=(Length[Select[$Packages,#=="FormTracer`"&]]>0);
FormTracerInstalled[]:=Module[{FTDirectory},
FTDirectory=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","FormTracer"}],
FileNameJoin[{$BaseDirectory,"Applications","FormTracer"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","FormTracer"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","FormTracer"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","FormTracer"}]
},
Select[$Path,StringContainsQ[#,"FormTracer"]&]
],
DirectoryQ[#]&
]<>"/"//Quiet;
If[Head[FTDirectory]=!=String,Return[False]];
Return[True];
];
If[Not@FormTracerInstalled[],
If[ChoiceDialog["FormTracer does not seem to be installed. Do you want to install it?",WindowTitle->"Install FormTracer",WindowSize->{Medium,All}],
Import["https://raw.githubusercontent.com/FormTracer/FormTracer/master/src/FormTracerInstaller.m"],
Print["The \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) package requires \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\) to run."];Abort[];
];
];
If[Not@FormTracerLoaded[],
Block[{Print},Get["FormTracer`"]];
If[FormTracerLoaded[],
Print["\!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\) package loaded. "];,
Print["Error: Could not load \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)package."];Abort[];
];
];
Block[{Print},FiniteT[True];]
Block[{Print},FastGamma5Trace[True];]
If[Head[$DistributedContexts]=!=List,$DistributedContexts={}];
$DistributedContexts=$DistributedContexts\[Union]{$Context,"TensorBases`Private`","TensorBases`","FormTracer`","FormTracer`Private`"}
Print["To see all (user-defined and package-defined) FormTracer definitions, call \!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"FormTracer\"].
Furthermore, \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\)\!\(\*
StyleBox[\" \",\nFontWeight->\"Bold\"]\)extends \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\). To see all extensions, call \!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"Extensions\"]"];
GetFormTracerGroups::usage="GetFormTracerGroups[]";
FormTracerGroupExistsQ::usage="GetFormTracerGroupList[name_Symbol]";
GetFormTracerGroupList::usage="GetFormTracerGroupList[name_Symbol]";
AddGroupTensors::usage="AddGroupTensors[groupDef_List]";
GetFormTracerGroupConstants::usage="GetFormTracerGroupConstants[]";
GetFormTracerGroupConstant::usage="GetFormTracerGroupConstant[name_Symbol]";
AddFormTracerGroup::usage="AddFormTracerGroup[{ingroupName_Symbol,inkind_Symbol,inconstant_}]";
UseLorentzLinearitySP::usage="";
UseLorentzLinearityVec::usage="";
UseLorentzLinearity::usage="";
TBInsertCombinedLorentzTensors::usage="";
ShowFormTracerExtensions[]:=Module[{},
Print["\!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) defines the following functions in extension to \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\) functionality.
In order to get detailed information on each of those, please call their usage messages, e.g. \!\(\*
StyleBox[\"GetFormTracerGroups\",\nFontColor->RGBColor[1, 0.5, 0]]\)::\!\(\*
StyleBox[\"usage\",\nFontColor->RGBColor[0, 0, 1]]\).
\!\(\*
StyleBox[\"GetFormTracerGroups\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"FormTracerGroupExists\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"GetFormTracerGroupList\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"AddGroupTensors\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"AddFormTracerGroup\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"GetFormTracerGroupConstants\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"GetFormTracerGroupConstant\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"UseLorentzLinearitySP\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"UseLorentzLinearityVec\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"UseLorentzLinearity\",\nFontColor->RGBColor[1, 0.5, 0]]\),
\!\(\*
StyleBox[\"TBInsertCombinedLorentzTensors\",\nFontColor->RGBColor[1, 0.5, 0]]\)"];
];
GetFormTracerGroups[]:=FormTracer`Private`groupNames;
FormTracerGroupExistsQ[name_Symbol]:=Module[{},
If[Not@MemberQ[GetFormTracerGroups[],name],
Return[False];,
Return[True];
];
];
GetFormTracerGroupTypes[]:=FormTracer`Private`groupTypes;
GetFormTracerGroupNamesAndTypes[]:=Transpose[{FormTracer`Private`groupNames,FormTracer`Private`groupTypes}]
GetFormTracerGroupList[name_Symbol]:=Module[{idx,type,constant,mRules,funcs},
If[Not@FormTracerGroupExistsQ[name],
Print["Logic error: "~~ToString[name]~~" is not an already defined group"];
Abort[];
];
idx=Flatten[Position[FormTracer`Private`groupNames,name]][[1]];
type=FormTracer`Private`groupTypes[[idx]];
constant=FormTracer`Private`groupConstantsTable[[idx]][[1]];
mRules=Select[Normal[FormTracer`Private`groupTensorReplacementRulesOutput],MemberQ[#,name,Infinity]&];
funcs=mRules//.(a_:>b_):>b//.a_[b___,FormTracer`Private`a$]->a[b,i,j,k];
Join[{type, {name, constant}},funcs]
];
AddGroupTensors[groupDef_List]:=Module[{alreadyPresent},
alreadyPresent=Map[GetFormTracerGroupList,FormTracer`Private`groupNames];
DefineGroupTensors[Join[
alreadyPresent,
{groupDef}
]]
]
GetFormTracerGroupConstants[]:=Module[{},
Return[FormTracer`Private`groupConstantsTable[[All,1]]];
];
GetFormTracerGroupConstant[name_Symbol]:=Module[{idx},
idx=Position[GetFormTracerGroups[],name][[1,1]];
Return[GetFormTracerGroupConstants[][[idx]]]
]
MakeConstant[name_Symbol]:=Module[{stripped},
Return[Symbol[SymbolName[name]]];
]
MakeConstant[number_Integer]:=number;
AddFormTracerGroup[{ingroupName_Symbol,inkind_Symbol,inconstant_}]:=Module[
{
groupName,kind,constant,args,
a,b,c
},
groupName=Symbol[SymbolName[ingroupName]];
kind=Symbol["FormTracer`"~~SymbolName[inkind]];
constant=Evaluate[Global`MakeConstant[inconstant]];
If[groupName===color,
Unprotect[color,Nc];
If[Not@FormTracerGroupExistsQ[color],
ClearAll[color];
Print["\!\(\*
StyleBox[\"Group\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"with\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"name\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"color\",\nFontSize->10,\nFontColor->RGBColor[0.5, 0, 0.5]]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"undefined\",\nFontSize->10]\)\!\(\*
StyleBox[\",\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"using\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"default\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"names\",\nFontSize->10]\)\!\(\*
StyleBox[\".\",\nFontSize->10]\)"];
If[IntegerQ[Nc]&&2<=Nc<=3,Print["Nc is set to ", Nc],
ClearAll[Nc]];
AddGroupTensors[{FormTracer`SUNfund, {color,Global`Nc}, deltaAdjCol[a, b], FCol[a, b, c], deltaFundCol[a, b], TCol[a, b, c],epsAdjCol[a, b, c], epsFundCol[a, b, c]}];
];
Protect[color,Nc];
Return[];
];
If[groupName===flavor,
Unprotect[flavor,Nf];
If[Not@FormTracerGroupExistsQ[flavor],
ClearAll[flavor];
Print["\!\(\*
StyleBox[\"Group\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"with\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"name\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"flavor\",\nFontSize->10,\nFontColor->RGBColor[0.5, 0, 0.5]]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"undefined\",\nFontSize->10]\)\!\(\*
StyleBox[\",\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"using\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"default\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"names\",\nFontSize->10]\)\!\(\*
StyleBox[\".\",\nFontSize->10]\)"];
If[IntegerQ[Nf]&&2<=Nf<=3,Print["Nc is set to ", Nc],
ClearAll[Nf]];
AddGroupTensors[{FormTracer`SUNfund, {flavor,Global`Nf}, deltaAdjFlav[a, b], FFlav[a, b, c], deltaFundFlav[a, b], TFlav[a, b, c], epsAdjFlav[a, b, c],epsFundFlav[a, b, c]}];
];
Protect[flavor,Nf];
Return[];
];
Unprotect[Evaluate[groupName]];
If[Not@FormTracerGroupExistsQ[groupName],
ClearAll[Evaluate[groupName]];
Print["\!\(\*
StyleBox[\"Group\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"with\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"name\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)"~~ToString[Style[ToString[groupName],Purple]]~~"\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"undefined\",\nFontSize->10]\)\!\(\*
StyleBox[\",\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"using\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"default\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"names\",\nFontSize->10]\)\!\(\*
StyleBox[\".\",\nFontSize->10]\)"];
If[IntegerQ[constant]&&2<=constant<=3,Print["Group constant is set to ", constant],
Unprotect[Evaluate[constant]];ClearAll[Evaluate[constant]]];
args={kind, {groupName,constant}, deltaAdj[groupName,a, b], F[groupName,a, b, c], deltaFund[groupName,a, b], T[groupName,a, b, c],epsAdj[groupName,a, b, c], epsFund[groupName,a, b, c]};
AddGroupTensors@args;
];
If[Not@IntegerQ[constant],Protect[constant]];
Protect[Evaluate[groupName]];
];
If[Length[Normal[FormTracer`Private`lorentzTensorReplacementRulesInput]]==0,
Print["\!\(\*
StyleBox[\"Lorentz\",\nFontSize->10,\nFontColor->RGBColor[0.5, 0, 0.5]]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"group\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"undefined\",\nFontSize->10]\)\!\(\*
StyleBox[\",\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"using\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"default\",\nFontSize->10]\)\!\(\*
StyleBox[\" \",\nFontSize->10]\)\!\(\*
StyleBox[\"names\",\nFontSize->10]\)\!\(\*
StyleBox[\".\",\nFontSize->10]\)"];
DefineLorentzTensors[deltaLorentz[mu, nu], vec[p, mu], sp[p, q], epsLorentz[i, j, k], deltaDirac[i, j], gamma[mu, i, j], gamma5[i, j], vecs[p, mu], sps[p, q]];
];
TBInsertOutputNaming[expr_]:=Module[
{outputRulesLorentzTensors,outputRulesGroupTensors,outputRules},
outputRulesLorentzTensors=Normal[FormTracer`Private`lorentzTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["Global`TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
outputRulesGroupTensors=Normal[FormTracer`Private`groupTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["Global`TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
outputRules=Join[outputRulesLorentzTensors,outputRulesGroupTensors];
Return[expr//.outputRules];
];
TBInsertLorentzNames[expr_]:=Module[
{outputNameRulesLorentzTensors},
outputNameRulesLorentzTensors=Normal[FormTracer`Private`lorentzTensorReplacementRulesOutput]/.{(a_[c___]:>b_[d___]):>(Symbol["Global`TB"~~StringSplit[ToString[a],"FTx"][[-1]]]:>b)};
Return[Evaluate[expr//.outputNameRulesLorentzTensors]];
]
Unprotect[UseLorentzLinearity,UseLorentzLinearitySP,UseLorentzLinearityVec];
UseLorentzLinearitySP[expr_]:=Module[{eval,conv=TBInsertLorentzNames},
SetAttributes[Evaluate[conv[TBsps]],Orderless];
SetAttributes[Evaluate[conv[TBsp]],Orderless];
conv[TBsp][0,a_]=0;
conv[TBsp][a_,0]=0;
conv[TBsp][0,0]=0;
conv[TBsps][0,a_]=0;
conv[TBsps][a_,0]=0;
conv[TBsps][0,0]=0;
conv[TBsp][a_,b_+c_]:= conv[TBsp][a,b]+conv[TBsp][a,c];
conv[TBsp][a_,-1b_]:= -conv[TBsp][a,b];
conv[TBsp][b_,a_?NumericQ c_]:= a conv[TBsp][b,c];
conv[TBsps][a_,b_+c_]:= conv[TBsps][a,b]+conv[TBsps][a,c];
conv[TBsps][a_,-1b_]:= -conv[TBsps][a,b];
conv[TBsps][b_,a_?NumericQ c_]:= a conv[TBsps][b,c];
eval=Evaluate[expr];
ClearAll[
Evaluate[conv[TBsps]],
Evaluate[conv[TBsp]]
];
Return[eval];
];
UseLorentzLinearityVec[expr_]:=Module[{eval,conv=TBInsertLorentzNames},
conv[TBvec][0,mu_]=0;
conv[TBvecs][0,mu_]=0;
conv[TBvecs][p_,0]=0;
conv[TBvec][p_+q_,mu_]:=conv[TBvec][p,mu]+conv[TBvec][q,mu];
conv[TBvec][-1 p_,mu_]:= -conv[TBvec][p,mu];
conv[TBvec][n_?NumericQ a_,mu_]:=n conv[TBvec][a,mu];
conv[TBvecs][p_+q_,mu_]:=conv[TBvecs][p,mu]+conv[TBvecs][q,mu];
conv[TBvecs][-1 p_,mu_]:= -conv[TBvecs][p,mu];
conv[TBvecs][n_?NumericQ a_,mu_]:=n conv[TBvecs][a,mu];
eval=Evaluate[expr];
ClearAll[
Evaluate[conv[TBvec]],
Evaluate[conv[TBvecs]]
];
Return[eval];
];
UseLorentzLinearity[expr_]:=UseLorentzLinearitySP[UseLorentzLinearityVec[expr]];
Protect[UseLorentzLinearity,UseLorentzLinearitySP,UseLorentzLinearityVec];
Unprotect[sigma,pdash,psdash];
sigma[v1_,v2_,d1_,d2_]:=Module[{dint1,dint2},TBInsertOutputNaming[I/2 (TBgamma[v1,d1,dint1]TBgamma[v2,dint1,d2]-TBgamma[v2,d1,dint2]TBgamma[v1,dint2,d2])]];pdash[p_,i_,j_]:=Module[{mu},TBInsertOutputNaming[TBgamma[mu,i,j]TBvec[p,mu]]];
psdash[p_,i_,j_]:=Module[{mu},TBInsertOutputNaming[TBgamma[mu,i,j]TBvecs[p,mu]]];
Protect[sigma,pdash,psdash];
TensorBases`Private`LTCache=
FormTracer`Private`combinedLorentzTensorInputCache;
removeObj[expr_]:=Module[{pos},
pos=FirstPosition[TensorBases`Private`LTCache,expr][[1]];
If[IntegerQ[pos],
TensorBases`Private`LTCache=Delete[TensorBases`Private`LTCache,pos]
];
];
removeObj/@{transProj[_,_,_],transProj[_,_,_,_],longProj[_,_,_],transProjMagnetic[_,_,_],transProjElectric[_,_,_]};
ClearAll[removeObj];
DefineCombinedLorentzTensors[
TBInsertOutputNaming[Union[
TensorBases`Private`LTCache,
{
(*zero temperature*)
{
transProj[p,mu,nu],
TBdeltaLorentz[mu,nu]-TBvec[p,mu]TBvec[p,nu]/TBsp[p,p]
},
{
transProj[p,q,mu,nu],
TBdeltaLorentz[mu,nu]-TBvec[p,mu]TBvec[q,nu]/TBsp[p,q]
},
{
longProj[p,mu,nu],
TBvec[p,mu]TBvec[p,nu]/TBsp[p,p]
},
(*finite temperature*)
{
transProjMagnetic[p,mu,nu],
TBdeltaLorentz[mu,nu]-(TBvecs[p,mu]TBvecs[p,nu])/TBsps[p,p]-TBdeltaLorentz[mu,0]*TBdeltaLorentz[nu,0]
},
{
transProjElectric[p,mu,nu],
TBdeltaLorentz[mu,0] TBdeltaLorentz[nu,0]-(TBvec[p,mu] TBvec[p,nu])/TBsp[p,p]+(TBvecs[p,mu] TBvecs[p,nu])/TBsps[p,p]
}
}
]]
];
TensorBases`Private`LTCache=
FormTracer`Private`lorentzTensorIdentitiesInputCache;
removeObj[expr_]:=Module[{pos},
pos=FirstPosition[TensorBases`Private`LTCache,expr][[1]];
If[IntegerQ[pos],
TensorBases`Private`LTCache=Delete[TensorBases`Private`LTCache,pos]
];
];
removeObj/@{transProj[_,_,_],transProj[_,_,_,_],longProj[_,_,_],transProjMagnetic[_,_,_],transProjElectric[_,_,_]};
ClearAll[removeObj];
DefineLorentzTensorIdentities[Union[TensorBases`Private`LTCache,{
(*zero temperature*)
{transProj[p,mu,rho]transProj[p,rho,nu],transProj[p,mu,nu]},
{transProj[p,mu,rho]transProj[p,nu,rho],transProj[p,mu,nu]},
{transProj[p,rho,mu]transProj[p,rho,nu],transProj[p,mu,nu]},
{longProj[p,mu,rho]longProj[p,rho,nu],longProj[p,mu,nu]},
{longProj[p,mu,rho]longProj[p,nu,rho],longProj[p,mu,nu]},
{longProj[p,rho,mu]longProj[p,rho,nu],longProj[p,mu,nu]},
{transProj[p,mu,rho]longProj[p,rho,nu],0},
{transProj[p,rho,mu]longProj[p,rho,nu],0},
{transProj[p,mu,rho]longProj[p,nu,rho],0},
(*finite temperature*)
{transProjMagnetic[p,mu,rho]transProjMagnetic[p,rho,nu],transProjMagnetic[p,mu,nu]},
{transProjMagnetic[p,mu,rho]transProjMagnetic[p,nu,rho],transProjMagnetic[p,mu,nu]},
{transProjMagnetic[p,rho,mu]transProjMagnetic[p,rho,nu],transProjMagnetic[p,mu,nu]},
{transProjElectric[p,mu,rho]transProjElectric[p,rho,nu],transProjElectric[p,mu,nu]},
{transProjElectric[p,mu,rho]transProjElectric[p,nu,rho],transProjElectric[p,mu,nu]},
{transProjElectric[p,rho,mu]transProjElectric[p,rho,nu],transProjElectric[p,mu,nu]},
{transProjMagnetic[p,mu,rho]transProjElectric[p,rho,nu],0},
{transProjMagnetic[p,mu,rho]transProjElectric[p,nu,rho],0},
{transProjMagnetic[p,rho,mu]transProjElectric[p,rho,nu],0},
{transProjMagnetic[p,mu,rho]longProj[p,rho,nu],0},
{transProjMagnetic[p,mu,rho]longProj[p,nu,rho],0},
{transProjMagnetic[p,rho,mu]longProj[p,rho,nu],0},
{transProjElectric[p,mu,rho]longProj[p,rho,nu],0},
{transProjElectric[p,mu,rho]longProj[p,nu,rho],0},
{transProjElectric[p,rho,mu]longProj[p,rho,nu],0}
}]
];
TBReplacementsLorentzTensors=Flatten[{
(*zero temperature*)
{transProj[p_,mu_,rho_]transProj[p_,rho_,nu_]:>transProj[p,mu,nu]},
{transProj[p_,mu_,rho_]transProj[p_,nu_,rho_]:>transProj[p,mu,nu]},
{transProj[p_,rho_,mu_]transProj[p_,rho_,nu_]:>transProj[p,mu,nu]},
{longProj[p_,mu_,rho_]longProj[p_,rho_,nu_]:>longProj[p,mu,nu]},
{longProj[p_,mu_,rho_]longProj[p_,nu_,rho_]:>longProj[p,mu,nu]},
{longProj[p_,rho_,mu_]longProj[p_,rho_,nu_]:>longProj[p,mu,nu]},
{transProj[p_,mu_,rho_]longProj[p_,rho_,nu_]:>0},
{transProj[p_,rho_,mu_]longProj[p_,rho_,nu_]:>0},
{transProj[p_,mu_,rho_]longProj[p_,nu_,rho_]:>0}
}];
TBCombinedLorentzTensorsList={
transProj[p_,mu_,nu_]:>TBInsertOutputNaming[TBdeltaLorentz[mu,nu]-TBvec[p,mu]TBvec[p,nu]/TBsp[p,p]],
transProj[p_,q_,mu_,nu_]:>TBInsertOutputNaming[TBdeltaLorentz[mu,nu]-TBvec[p,mu]TBvec[q,nu]/TBsp[p,q]],
longProj[p_,mu_,nu_]:>TBInsertOutputNaming[TBvec[p,mu]TBvec[p,nu]/TBsp[p,p]],
(*finite temperature*)
transProjMagnetic[p_,mu_,nu_]:>TBInsertOutputNaming[TBdeltaLorentz[mu,nu]-(TBvecs[p,mu]TBvecs[p,nu])/TBsps[p,p]-TBdeltaLorentz[mu,0]*TBdeltaLorentz[nu,0]],
transProjElectric[p_,mu_,nu_]:>TBInsertOutputNaming[TBdeltaLorentz[mu,0] TBdeltaLorentz[nu,0]-(TBvec[p,mu] TBvec[p,nu])/TBsp[p,p]+(TBvecs[p,mu] TBvecs[p,nu])/TBsps[p,p]]
};
TBInsertCombinedLorentzTensors[expr_]:=expr//.TBReplacementsLorentzTensors//.TBCombinedLorentzTensorsList;
ShowFormTracerDefinitions[]:=Module[{els},
Print["FormTracer Names: ",TableForm[Join[
{
{"\!\(\*SubscriptBox[\(\[Delta]\), \(ij\)]\) in Lorentz group",TBdeltaLorentz[i,j]},
{"\!\(\*SubscriptBox[\(p\), \(\[Mu]\)]\) Lorentz vector",TBvec[p,\[Mu]]},
{"\!\(\*SubscriptBox[\(p\), \(i\)]\) spatial Lorentz vector",TBvecs[p,i]},
{"\!\(\*SubscriptBox[\(p\), \(\[Mu]\)]\)\!\(\*SubscriptBox[\(q\), \(\[Mu]\)]\) scalar product",TBsp[p,q]},
{"\!\(\*SubscriptBox[\(p\), \(i\)]\)\!\(\*SubscriptBox[\(q\), \(i\)]\) spatial calar product ",TBsps[p,q]},
{"",""},
{"\!\(\*SubscriptBox[\(\[Delta]\), \(ij\)]\) in Spinor group",TBdeltaDirac[i,j]},
{"\!\(\*SubscriptBox[\(\[Gamma]\), \(\[Mu]\)]\)",TBgamma[\[Mu],d1,d2]},
{"\!\(\*SubscriptBox[\(\[Gamma]\), \(5\)]\)",TBgamma5[d1,d2]},
{"\!\(\*SubscriptBox[\(\[Epsilon]\), \(\[Mu]\[Nu]\[Rho]\)]\)",TBepsLorentz[\[Mu],\[Nu],\[Rho]]},
{"",""}
},
Flatten[Map[{
{"adjoint \!\(\*SubscriptBox[\(\[Delta]\), \(ab\)]\)",TBdeltaAdj[#,a,b]},
{"fundamental \!\(\*SubscriptBox[\(\[Delta]\), \(AB\)]\)",TBdeltaFund[#,A,B]},
{"\!\(\*FractionBox[SubscriptBox[\(f\), \(abc\)], \(2\)]\)",TBF[#,a, b, c]},
{"(\!\(\*SubscriptBox[\(t\), \(a\)]\)\!\(\*SubscriptBox[\()\), \(BC\)]\)",TBT[#,a, B, C]},
{"\!\(\*SubscriptBox[\(\[Epsilon]\), \(abc\)]\)",TBepsAdj[#,a, b, c]},
{"\!\(\*SubscriptBox[\(\[Epsilon]\), \(ABC\)]\)",TBepsFund[#,A, B, C]},
{"group constant",GetFormTracerGroupConstant[#]},
{"",""}}&,GetFormTracerGroups[]],1]
]//TBInsertOutputNaming
,TableHeadings->{Join[
{"Lorentz","","","","","",
"spinor","","","",""},
Flatten[Map[{#,"","","","","","",""}&,
Map[ToString[#[[1]]]<>"("<>ToString[#[[2]]]<>")"&,GetFormTracerGroupNamesAndTypes[]]
],1]
]
, {"object","name"}},TableSpacing->{3, 3}]];
els=Transpose[{
TBCombinedLorentzTensorsList//.(a_[b___]:>f_):>a@@ToExpression[StringReplace[ToString[{b}],"_"->""]],
TBCombinedLorentzTensorsList//.(a_[b___]:>f_):>f
}];
Print["\nCombined Lorentz tensors: ",TableForm[Transpose[{els[[All,2]]}],TableHeadings->{els[[All,1]],{"replacement","name"}},TableSpacing->{3, 5}]];
Print["\nThese can be explicitly evaluated by using e.g. \!\(\*
StyleBox[\"TBInsertCombinedLorentzTensors\",\nFontColor->RGBColor[1, 0.5, 0]]\)[transProj[p,\[Mu],\[Nu]]]"];
Print["\n
TensorBases defines additionally the following Lorentz tensors:
sigma[\[Mu],\[Nu],\!\(\*SubscriptBox[\(d\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \(2\)]\)] : \!\(\*FractionBox[\(\[ImaginaryI]\), \(2\)]\)[\!\(\*SubscriptBox[\(\[Gamma]\), \(\[Mu]\)]\),\!\(\*SubscriptBox[\(\[Gamma]\), \(\[Nu]\)]\)\!\(\*SubscriptBox[\(]\), \(\*SubscriptBox[\(d\), \(1\)] \*SubscriptBox[\(d\), \(2\)]\)]\)
pdash[p,\!\(\*SubscriptBox[\(d\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \(2\)]\)] : (\!\(\*SubscriptBox[\(\[Gamma]\), \(\[Mu]\)]\)\!\(\*SubscriptBox[\(p\), \(\[Mu]\)]\)\!\(\*SubscriptBox[\()\), \(\*SubscriptBox[\(d\), \(1\)] \*SubscriptBox[\(d\), \(2\)]\)]\)
psdash[p,\!\(\*SubscriptBox[\(d\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \(2\)]\)] : (\!\(\*SubscriptBox[\(\[Gamma]\), \(i\)]\)\!\(\*SubscriptBox[\(p\), \(i\)]\)\!\(\*SubscriptBox[\()\), \(\*SubscriptBox[\(d\), \(1\)] \*SubscriptBox[\(d\), \(2\)]\)]\)
"];
];
BeginPackage["TensorBases`"];
Unprotect["TensorBases`*"];
Unprotect["TensorBases`Private`*"];
ClearAll["TensorBases`*"];
ClearAll["TensorBases`Private`*"];
If[Head[$DistributedContexts]=!=List,$DistributedContexts={}];
$DistributedContexts=$DistributedContexts\[Union]{$Context,"TensorBases`Private`","TensorBases`","FormTracer`","FormTracer`Private`"}
TBGetBasisElement::usage = "\!\(\*
StyleBox[\"TBGetBasisElement\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,n_Integer,indices___]
Obtains the n-th element of the specified basis. The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.
\!\(\*
StyleBox[\"TBGetBasisElement\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,All,indices___]
Returns a list with all elements of the specified basis. The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.";
TBGetVertex::usage = "\!\(\*
StyleBox[\"TBGetVertex\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,n_Integer,indices___]
Obtains the n-th vertex of the specified basis. The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.
\!\(\*
StyleBox[\"TBGetVertex\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,All,indices___]
Returns a list with all vertices of the specified basis. The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.";
TBGetInnerProduct::usage = "\!\(\*
StyleBox[\"TBGetInnerProduct\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String]
Returns the bilinear operator \!\(\*
StyleBox[\"\[ScriptCapitalO]\",\nFontColor->RGBColor[0.5, 0, 0.5]]\) that represents the inner product of the specified basis.
It can be called as \!\(\*
StyleBox[\"\[ScriptCapitalO]\",\nFontColor->RGBColor[0.5, 0, 0.5]]\)[Tensor1, n, Tensor2, m], where Tensor1 and Tensor2 are functions with signatures Tensor[BasisName_String, n_Integer, indices___].
For example, \!\(\*
StyleBox[\"\[ScriptCapitalO]\",\nFontColor->RGBColor[0.5, 0, 0.5]]\)[\!\(\*
StyleBox[\"TBGetBasisElement\",\nFontColor->RGBColor[1, 0.5, 0]]\), 1, \!\(\*
StyleBox[\"TBGetBasisElement\",\nFontColor->RGBColor[1, 0.5, 0]]\), 1] returns <\!\(\*SubscriptBox[\(e\), \(i\)]\),\!\(\*SubscriptBox[\(e\), \(j\)]\)>.";
TBGetMetric::usage = "\!\(\*
StyleBox[\"TBGetMetric\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String]
Returns the metric of the specified basis, i.e. the matrix \!\(\*SubscriptBox[\(g\), \(ij\)]\) = <\!\(\*SubscriptBox[\(e\), \(i\)]\),\!\(\*SubscriptBox[\(e\), \(j\)]\)>, where the \!\(\*SubscriptBox[\(e\), \(i\)]\) are the basis elements of the basis.";
TBGetInverseMetric::usage = "\!\(\*
StyleBox[\"TBGetInverseMetric\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String]
Returns the inverse of the metric of the specified basis, i.e. the matrix \!\(\*SuperscriptBox[SubscriptBox[\(g\), \(ij\)], \(-1\)]\) = (<\!\(\*SubscriptBox[\(e\), \(i\)]\),\!\(\*SubscriptBox[\(e\), \(j\)]\)>\!\(\*SuperscriptBox[\()\), \(-1\)]\), where the \!\(\*SubscriptBox[\(e\), \(i\)]\) are the basis elements of the basis.";
TBGetProjector::usage = "\!\(\*
StyleBox[\"TBGetBasisProjector\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,n_Integer,indices___]
Returns the n-th projector, which is defined by \!\(\*SuperscriptBox[SubscriptBox[\(g\), \(nj\)], \(-1\)]\)\!\(\*SubscriptBox[\(e\), \(j\)]\). The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.
\!\(\*
StyleBox[\"TBGetVertex\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,All,indices___]
Returns a list with all projectors of the specified basis, defined by \!\(\*SuperscriptBox[SubscriptBox[\(g\), \(nj\)], \(-1\)]\)\!\(\*SubscriptBox[\(e\), \(j\)]\). The given indices must match the ones specified by the basis, see TBInfo[].
If no indices are given, the standard indices specified by the basis are used.";
TBInfo::usage = "\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[_String]
Return information on a given object.
\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[] prints all available bases with some usage information.
\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName] prints detailed information provided by this basis.
\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"FormTracer\"] prints all defined groups and identites which \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\) currently knows.
\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"Extensions\"] prints all extensions to \!\(\*
StyleBox[\"FormTracer\",\nFontWeight->\"Bold\"]\), defined by the \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) package.
\!\(\*
StyleBox[\"TBInfo\",\nFontColor->RGBColor[1, 0.5, 0]]\)[\"Momenta\"] prints all momentum transformations that can be performed by the \!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) package.";
TBImportBasis::usage = "\!\(\*
StyleBox[\"TBImportBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisDefinitionFile_String,CacheDirectory_String:\"./TBCache\"]
Import a custom basis definition file. The optional argument CacheDirectory can be set to choose a specific location where the intermediate files from processing the basis are stored."
TBExportBasis::usage = "\!\(\*
StyleBox[\"TBExportBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,folder_String:\"./\"]
Export a basis definition file. The basis with the name BasisName has to be loaded in memory. If the optional argument folder is given, this will be the location where the exported basis definition will be placed."
TBRestrictBasis::usage = "\!\(\*
StyleBox[\"TBRestrictBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)[inBasisName_String, outBasisName_String, {indices__Integer}, CacheDirectory_String:\"./TBCache\"]
Restrict an existing basis. The new basis will be called outBasisName and only contain the basis elements specified by the given indices."
TBConstructBasis::usage = "\!\(\*
StyleBox[\"TBConstructBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)[
BasisName_String,\[IndentingNewLine] {RequiredGroups___List},
VertexName_String,
VertexStructure_,
InnerProduct_,
Comment_String,
Author_String,
Usage_,
{Indices__List},
MomentumConservation_List,
{Tensors__List},
Replacements_List,
CacheDirectory_String:\"./TBCache\"
]
Construct a new basis from a given set of Tensors.
"
TBExportCache::usage = "\!\(\*
StyleBox[\"TBExportCache\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String,CacheFolder_String:\"./TBCache\"]
Exports everything in memory of the Basis BasisName onto disk in the folder CacheFolder.
"
TBUnregister::usage = "\!\(\*
StyleBox[\"TBUnregister\",\nFontColor->RGBColor[1, 0.5, 0]]\)[BasisName_String]
Remove an existing basis from internal memory. This does not delete or change any files on disk."
TB3PToS0S1SPhi::usage="TB3PToS0S1SPhi[p1_Symbol,p2_Symbol,p3_Symbol,S0_Symbol,S1_Symbol,SPhi_Symbol]";
TB3PFromS0S1SPhi::usage="TB3PFromS0S1SPhi[p1_Symbol,p2_Symbol,p3_Symbol,S0_Symbol,S1_Symbol,SPhi_Symbol]";
TB3PToS0S1SPhiQk::usage="TB3PToS0S1SPhi[Q_Symbol,k_Symbol,S0_Symbol,S1_Symbol,SPhi_Symbol]";
TB3PFromS0S1SPhiQk::usage="TB3PFromS0S1SPhi[Q_Symbol,k_Symbol,S0_Symbol,S1_Symbol,SPhi_Symbol]";
TB3PToS0as::usage="TB3PToS0as[p1_Symbol,p2_Symbol,p3_Symbol,S0_Symbol,a_Symbol,s_Symbol]";
TB3PFromS0as::usage="TB3PFromS0as[p1_Symbol,p2_Symbol,p3_Symbol,S0_Symbol,a_Symbol,s_Symbol]";
TBProjectToSymmetricPoint::usage="TBProjectToSymmetricPoint[expr_,q_Symbol,p_Symbol,momenta___Symbol]";
TBProjectToSymmetricPointSpatial::usage="TBProjectToSymmetricPointSpatial[expr_,q_Symbol,p_Symbol,momenta___Symbol]";
TBInfo["FormTracer"]:=Global`ShowFormTracerDefinitions[];
TBInfo["Extensions"]:=Global`ShowFormTracerExtensions[];
TBInfo["BaseBuilder"]:=Print@"\!\(\*
StyleBox[\"TensorBases\",\nFontWeight->\"Bold\"]\) provides facilities for exporting and importing bases:
\n\!\(\*
StyleBox[\"TBImportBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\) and\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\"TBExportBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)allow for importing user-written basis definition files and automatic export of bases in memory to such definition files.
\n\!\(\*
StyleBox[\"TBExportCache\",\nFontColor->RGBColor[1, 0.5, 0]]\) writes any basis data in memory to disk at a specified location.
\n\!\(\*
StyleBox[\"TBUnregister\",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)allows to remove basis names from the registry, which allows one to overwrite bases by custom imports.
\n\!\(\*
StyleBox[\"TBRestrictBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)creates a new basis from an old one by simple restriction.
\n\!\(\*
StyleBox[\"TBConstructBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0.5, 0]]\)creates a new basis from a set of primitive tensors. The method automatically takes tensor products of multiple given tensor spaces and reduces any overcomplete set using a given inner product to a minimal basis (a maximal linearly independent set).
\nFor usage help with the aforementioned functions, please call their usage messages, e.g. \!\(\*
StyleBox[\"TBConstructBasis\",\nFontColor->RGBColor[1, 0.5, 0]]\)::\!\(\*
StyleBox[\"usage\",\nFontColor->RGBColor[0, 0, 1]]\).
"
Begin["`Private`"];
If[Head[$DistributedContexts]=!=List,$DistributedContexts={}];
$DistributedContexts=$DistributedContexts\[Union]{$Context,"TensorBases`Private`","TensorBases`","FormTracer`","FormTracer`Private`"}
GlobalContext[expr_]:=Module[{$ContextOld,result},
$ContextOld=$Context;
$Context="Global`";
result=ReleaseHold[expr];
$Context=$ContextOld;
Return[result];
];
SetAttributes[GlobalContext,HoldAll]
WithinContext[context_String,expr_]:=Module[{$ContextOld,result},
$ContextOld=$Context;
$Context=context;
Begin[context];
Print["Changed to context", $Context];
result=ReleaseHold[expr];
End[];
$Context=$ContextOld;
Return[result];
];
SetAttributes[WithinContext,HoldRest]
FormTracerNaming[]:=Module[
{outputRulesLorentzTensors,outputRulesGroupTensors,outputRules,
privateOutputRulesLorentzTensors,privateOutputRulesGroupTensors,privateOutputRules},
outputRulesLorentzTensors=Normal[FormTracer`Private`lorentzTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c])};
outputRulesGroupTensors=Normal[FormTracer`Private`groupTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c])};
outputRules=Join[outputRulesLorentzTensors,outputRulesGroupTensors];
Print["Lorentz group: ",outputRulesLorentzTensors//TableForm];
Print[""];
Print["color group: ",Select[outputRulesGroupTensors,MemberQ[#,Global`color,Infinity]&]//TableForm];
Print[""];
Print["flavor group: ",Select[outputRulesGroupTensors,MemberQ[#,Global`flavor,Infinity]&]//TableForm];
];
InsertOutputNaming[expr_]:=Module[
{
groups,
outputRulesLorentzTensors,outputRulesGroupTensors,outputRules,
privateOutputRulesLorentzTensors,privateOutputRulesGroupTensors,privateOutputRules,
otherRules
},
outputRulesLorentzTensors=Normal[FormTracer`Private`lorentzTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
outputRulesGroupTensors=Normal[FormTracer`Private`groupTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
outputRules=Join[outputRulesLorentzTensors,outputRulesGroupTensors];
privateOutputRulesLorentzTensors=Normal[FormTracer`Private`lorentzTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TensorBases`Private`TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
privateOutputRulesGroupTensors=Normal[FormTracer`Private`groupTensorReplacementRulesOutput]/.{(a_[c___]:>b_):>(Symbol["TensorBases`Private`TB"~~StringSplit[ToString[a],"FTx"][[-1]]][c]:>b)};
privateOutputRules=Join[privateOutputRulesLorentzTensors,privateOutputRulesGroupTensors];
groups={
TensorBases`Private`flavor->Global`flavor,
TensorBases`Private`color->Global`color
};
otherRules={
TensorBases`Private`sigma:>Global`sigma,
TensorBases`Private`pdash:>Global`pdash,
TensorBases`Private`psdash:>Global`psdash,
TensorBases`Private`transProj:>Global`transProj,
TensorBases`Private`longProj:>Global`longProj,
TensorBases`Private`transProjMagnetic:>Global`transProjMagnetic,
TensorBases`Private`transProjElectric:>Global`transProjElectric
};
Return[expr//.groups//.outputRules//.privateOutputRules//.otherRules/.a_Symbol/;Context[a]=="TensorBases`Private`":>Symbol["Global`"~~SymbolName[a]]];
];
InsertInputNaming[expr_]:=Module[
{
inputRulesLorentzTensors,inputRulesGroupTensors
},
inputRulesLorentzTensors=Select[Normal[FormTracer`Private`lorentzTensorReplacementRulesInput],MatchQ[_[__]:>_[__]]]/.{
(a_[d__]:>b_[c__]):>(a[d]->Symbol["TB"~~StringSplit[ToString[b],"FTx"][[-1]]][c])
};
inputRulesGroupTensors=Select[Normal[FormTracer`Private`groupTensorReplacementRulesInput],MatchQ[_[__]:>_[__]]]/.{
(a_[d__]:>b_[c__]):>(a[d]->Symbol["TB"~~StringSplit[ToString[b],"FTx"][[-1]]][c])
};
Return[expr//.inputRulesLorentzTensors//.inputRulesGroupTensors];
];
TBFormTrace[expr_]:=Module[{processedExpr,result},
processedExpr=InsertOutputNaming[expr];
result=GlobalContext[FormTracer`FormTrace[processedExpr]];
Return[result];
];
SetAttributes[TBsps,Orderless]
SetAttributes[TBsp,Orderless]
TBsp[0,a_]=0;
TBsp[a_,0]=0;
TBsp[0,0]=0;
TBsps[0,a_]=0;
TBsps[a_,0]=0;
TBsps[0,0]=0;
TBvec[0,mu_]=0;
TBvecs[0,mu_]=0;
TBvecs[p_,0]=0;
TBsp[a_,b_+c_]:= TBsp[a,b]+TBsp[a,c];
TBsp[a_,-1b_]:= -TBsp[a,b];
TBsp[b_,a_?NumericQ c_]:= a TBsp[b,c];
TBsps[a_,b_+c_]:= TBsps[a,b]+TBsps[a,c];
TBsps[a_,-1b_]:= -TBsps[a,b];
TBsps[b_,a_?NumericQ c_]:= a TBsps[b,c];
TBvec[p_+q_,mu_]:=TBvec[p,mu]+TBvec[q,mu];
TBvec[-1 p_,mu_]:= -TBvec[p,mu];
TBvec[n_?NumericQ a_,mu_]:=n TBvec[a,mu];
TBvecs[p_+q_,mu_]:=TBvecs[p,mu]+TBvecs[q,mu];
TBvecs[-1 p_,mu_]:= -TBvecs[p,mu];
TBvecs[n_?NumericQ a_,mu_]:=n TBvecs[a,mu];
Unprotect[TBPrint];
TBPrint[thing_,level_Integer]:=If[IntegerQ[Global`TBVerbose]&&Global`TBVerbose>=level,Print[thing]];TBPrint[thing_List,level_Integer]:=If[IntegerQ[Global`TBVerbose]&&Global`TBVerbose>=level,Print@@thing];
Protect[TBPrint];
AlreadyUnique[x_Symbol]:=Module[{split,tailNumbers},
split=StringSplit[ToString[x],"$"];
If[Length[split]==1,Return[False]];
tailNumbers=DigitQ[split[[-1]]];
Return[tailNumbers];
]
UniqueStem[x_Symbol]:=Module[{split},
split=StringSplit[ToString[x],"$"];
Return[split[[1]]];
]
TBUnique[x_Symbol]:=Module[{},
Return[
Unique[Symbol[UniqueStem[x]]]
];
]
GetAllSymbols[expr_]:=DeleteDuplicates@Cases[{expr},_Symbol,Infinity]
MakeIndexList[len_Integer,expr___]:=Module[{list},
If[Length[{expr}]==1&&Head[{expr}[[1]]]===List,
list=expr,
list={expr}
];
If[Length[list]==0,Print["Index list is empty!"];Abort[];];
If[Length[list]!=len,Print["Index list must have "~~ToString[len]~~" elements!"];Abort[];];
If[AnyTrue[list,Head[#]=!=List&],Print["An index list must consist of one list for every particle!"];Abort[];];
Return[list];
]
(* ::Input::Initialization:: *)
TBDirectory=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","TensorBases"}],
FileNameJoin[{$BaseDirectory,"Applications","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","TensorBases"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","TensorBases"}]
},
Select[$Path,StringContainsQ[#,"TensorBases"]&]
],
DirectoryQ[#]&
]<>"/";
If[Head[TBDirectory]=!=String,
Print["\n!!!!!!!!!!\nCannot find valid TensorBases installation! Cached tensor data is not available, loading the package may take an extremely long time.\n!!!!!!!!!!\n"]
];
AutoSaveRestore[fileName_String,expr_,dir_String:TBDirectory]:=Module[{mdir,file,ret},
mdir=ReleaseHold[dir];
If[StringTake[mdir,{-1}]!="/",mdir=StringJoin[mdir,"/"]];
file=mdir<>fileName<>".m";
If[FileExistsQ[file],
ret=Import[file];
,
ret=ReleaseHold[expr];
Export[file,ret];
];
Return[ret];
];
SetAttributes[AutoSaveRestore,HoldRest]
TBGetBasisElement[name_String,All,indices___]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetBasisElement[name_String,n_Integer,indices___]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetBasisElement[name_String,All]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetBasisElement[name_String,n_Integer]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetBasisElement[name_String]:=Module[{},
Print["TBGetBasisElement[...] requires at least two arguments! Aborting"];Abort[]
];
TBGetBasisElement[]:=Module[{},
Print["TBGetBasisElement[...] requires at least two arguments! Aborting"];Abort[]
];
TBGetVertex[name_String,All,indices___]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetVertex[name_String,n_Integer,indices___]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetVertex[name_String,All]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetVertex[name_String,n_Integer]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetVertex[name_String]:=Module[{},
Print["TBGetVertex[...] requires at least two arguments! Aborting"];Abort[]
];
TBGetVertex[]:=Module[{},
Print["TBGetVertex[...] requires at least two arguments! Aborting"];Abort[]
];
TBGetMetric[name_String]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetMetric[]:=Module[{},
Print["TBGetMetric[...] requires an argument. Aborting"];Abort[]
];
TBGetInverseMetric[name_String]:=Module[{},
Print["Unknown basis "~~name~~". Aborting"];Abort[]
];
TBGetInverseMetric[]:=Module[{},
Print["TBGetInverseMetric[...] requires an argument. Aborting"];Abort[]
];
TBGetProjector[name_String,All,indices___]:=Module[{},