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QMeSderivation.m
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QMeSderivation.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. *)
(************************************************************************)
(* ::Input::Initialization:: *)
Needs["QMeSderivation`Tools`"]
(* ::Input::Initialization:: *)
BeginPackage["QMeSderivation`"]
(* ::Input::Initialization:: *)
$DistributedContexts:={$Context,"QMeSderivation`","QMeSderivation`Private`"};
(* ::Input::Initialization:: *)
DeriveFunctionalEquation::usage = "DeriveFunctionalEquation[setup, derivativelist, options]
If you already have a master equation the setup is:
setup = <|\"MasterEquation\" -> masterEquation, \"FieldSpace\" -> fields, \"Truncation\" -> truncation|>
If you first want to derive the DSE for a theory:
SetupDSE = <|\"MasterEquation\" -> <|\"getDSE\" -> \"True\", \"classicalAction\" -> classicalAction|>,
\"FieldSpace\" -> fields, \"Truncation\" -> truncation|>
Master equations can be the FRG equation:
FRGEq = {\"Prefactor\" -> {1/2}, <|\"type\" -> \"Regulatordot\", \"indices\" -> {a, b}|>,
<|\"type\" -> \"Propagator\", \"indices\" -> {a, b}|>}
or the mSTI:
LHSmSTIEq = {\"Prefactor\" -> {1}, <|\"type\" -> \"nPoint\", \"indices\" -> {Q[i]}, \"nPoint\" -> 1, \"spec\" -> \"BRST\"|>, <|\"type\" -> \"nPoint\", \"indices\" -> {i}, \"nPoint\" -> 1, \"spec\" -> \"none\"|>,}
mSTIEq = {\"Prefactor\" -> {1}, <|\"type\" -> \"Regulator\", \"indices\" -> {a, b}|>,
<|\"type\" -> \"Propagator\", \"indices\" -> {b, c}|>,
<|\"type\" -> \"nPoint\", \"indices\" -> {c, Q[a]}, \"nPoint\" -> 2, \"spec\" -> \"BRST\"|>}
One specifies the theory by giving a list of fields (and BRST sources) with their respective indices and statistics. If no bosonic or fermionic fields are present in a theory one must insert an empty list.
fields = <|\"bosonic\" -> {A[p, {mu, i}], B[p,{i}]},
\"fermionic\" -> {{cbar[p, {i}], c[p, {i}]}, {af[p,{i}], f[p,{i}]}},
\"BRSTsources\" -> {{Q[A], \"fermionic\"}, {Q[B], \"fermionic\"}, {Q[cbar], \"bosonic\"}, {Q[c], \"bosonic\"}, {Q[af], \"bosonic\"}, {Q[f], \"bosonic\"}}|>
The classical action and truncation are simply a list of possible vertices starting with the possible propagators.
classicalAction = {{A, A}, {c, cbar}, {A, A, A}, {A, A, A, A}, {A, c, cbar}}
truncation = {{A, A}, {c, cbar}, {A, A, A}, {A, A, A, A}, {A, c, cbar}, {A, A, c, cbar}}
For the list of derivatives one generally has three options:
DerivativeList1 = {A, A}
DerivativeList2 = {A[a], A[b]}
DerivativeList3 = {A[-p, {mu, m}], A[p, {nu, n}]}
The options for the function getFunctionalDerivatives are:
\"OutputLevel\" -> \"getDSE\"
\"OutputLevel\" -> \"FunctionalDerivatives\"
\"OutputLevel\" -> \"SuperindexDiagrams\"
\"OutputLevel\" -> \"FullDiagrams\"
DerivativeList1 works with the first two output levels, DerivativeList2 with the first three and DerivativeList3 works for all output levels.
\"getDSE\": Computes the DSE of the theory
\"FunctionalDerivatives\": Takes functional derivatives of the master equation
\"SuperindexDiagrams\": Takes the trace in field space and sorts the objects
\"FullDiagrams\": replaces the superfield indices with physical indices and writes the objects as funtions
";
(* ::Input::Initialization:: *)
getDSE::usage = "getDSE[classicalAction, firstDerivative]
Derive the DSE for a given classical action. A simple example is
getDSE[{{phi,phi},{phi,phi,phi,phi}}, phi[a]]
";
(* ::Input::Initialization:: *)
SuperindexToFullDiagrams::usage = "SuperindexToFullDiagrams[diagrams,setup, derivativelist, options]
Insert the physical indices and momentum routing into a list of superindex diagrams.
";
(* ::Input::Initialization:: *)
Begin["`Private`"]
(* ::Input::Initialization:: *)
qmesDerivationDirectory=SelectFirst[
Join[
{
FileNameJoin[{$UserBaseDirectory,"Applications","QMeSderivation"}],
FileNameJoin[{$BaseDirectory,"Applications","QMeSderivation"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Applications","QMeSderivation"}],
FileNameJoin[{$InstallationDirectory,"AddOns","Packages","QMeSderivation"}],
FileNameJoin[{$InstallationDirectory,"AddOns","ExtraPackages","QMeSderivation"}]
},
Select[$Path,StringContainsQ[#,"QMeS-Derivation"]&]
],
DirectoryQ[#]&
];
(* ::Input::Initialization:: *)
$DebugLevel =0;
(* ::Input::Initialization:: *)
myEcho[msg_,lvl_] := If[$DebugLevel >=lvl, Echo[msg];, Nothing;]
(* ::Input::Initialization:: *)
Clear[getDSE]
getDSE[classicalAction_,firstDerivative_] := Module[{fullClassicalAction,derAction,rhsExpDSE,rhsDSE},
fullClassicalAction = generateClassicalAction[classicalAction];
derAction = takeFieldDerivative[fullClassicalAction,firstDerivative];
rhsExpDSE = replaceExpectationValue[derAction];
rhsDSE = takeFinalFieldDerivatives[rhsExpDSE]/."dummyEntry"->Nothing;
Return[rhsDSE]
]
(* ::Input::Initialization:: *)
(*generate the classical action in operator and list form form with superfield indices*)
Clear[generateClassicalAction]
generateClassicalAction[classicalAction_] := Module[{},
generateClassicalAction[{},classicalAction]
]
generateClassicalAction[actionList_,classicalAction_] := Module[{newTerm,newactionList,newclassicalAction},
newTerm = transformToClassicalObject[classicalAction[[1]]];
newactionList = Join[actionList,{newTerm}];
newclassicalAction = classicalAction[[2;;-1]];
generateClassicalAction[newactionList,newclassicalAction]
]
generateClassicalAction[actionList_,{}] := Module[{},
Return[actionList]
]
(* ::Input::Initialization:: *)
(*transform list of vertices into objects*)
Clear[transformToClassicalObject]
transformToClassicalObject[classicalActionEntry_] := Module[{objectList,objectsIndices,fullObjectList, prefac},
objectList = (<|"type"-> "classicalField", "indices"-> {classicalActionEntry[[#]][Unique[Global`a83]]}|>)&/@Range[Length@classicalActionEntry];
objectsIndices = Evaluate[Reverse@objectList[[All,"indices"]]][[All,1]];
prefac = getPrefactor[classicalActionEntry];
fullObjectList = Join[{"Prefactor"-> {prefac},<|"type"->"nPoint","indices"->objectsIndices,"nPoint"-> Length@objectList,"spec"->"classical"|>},objectList];
Return[fullObjectList]
]
(* ::Input::Initialization:: *)
(*get correct 1/n! prefactors*)
Clear[getPrefactor]
getPrefactor[classicalActionEntry_] := Module[{modFieldList,prefacList,prefac},
modFieldList = Split[classicalActionEntry];
prefacList = 1/((Length[#]&/@modFieldList)!);
prefac = Times@@prefacList;
Return[prefac]
]
(* ::Input::Initialization:: *)
(*get correct 1/n! prefactors*)
Clear[getSign]
getSign[classicalActionEntry_] := Module[{sign},
sign = generatePrefacCombinations[classicalActionEntry];
Return[sign]
]
(* ::Input::Initialization:: *)
(*generate the classical action in operator and list form form with superfield indices*)
Clear[generatePrefacCombinations]
generatePrefacCombinations[classicalActionEntry_] := Module[{},
generatePrefacCombinations[classicalActionEntry,{}]
]
generatePrefacCombinations[classicalActionEntry_,prefac_] := Module[{newCombinations,newactionList,combinations},
newactionList= classicalActionEntry[[1;;-2]];
newCombinations = Tuples[{newactionList,classicalActionEntry[[{-1}]]}];
combinations = Join[prefac,newCombinations];
generatePrefacCombinations[newactionList,combinations]
]
generatePrefacCombinations[{},actionList_] := Module[{},
Return[actionList]
]
(* ::Input::Initialization:: *)
Clear[takeFieldDerivative]
takeFieldDerivative[fullClassicalAction_,firstDerivative_]:=Module[{},
takeFieldDerivative[{},fullClassicalAction,firstDerivative]
]
takeFieldDerivative[derAction_,restClassicalAction_,firstDerivative_] := Module[{newDerAction,newrestClassicalAction},
newrestClassicalAction = restClassicalAction[[2;;-1]];
newDerAction = Join[derAction,takeOneFieldDerivative[restClassicalAction[[1]],firstDerivative]];
takeFieldDerivative[newDerAction,newrestClassicalAction,firstDerivative]
]
takeFieldDerivative[derAction_,{},firstDerivative_] := Module[{},
Return[derAction]
]
(* ::Input::Initialization:: *)
Clear[takeOneFieldDerivative]
takeOneFieldDerivative[oneActionTerm_,firstDerivative_]:=Module[{derTerm, fieldObject,derField,derAction,deltaIndices,dummyaaa,startingPrefactor,prefactors,newfullPrefactor},
If[(Length@firstDerivative)==0,
derField = firstDerivative;
,
derField = Head@firstDerivative;
];
startingPrefactor = oneActionTerm[[1]];
derAction = (fieldObject =oneActionTerm[[2+#]];
If[ToString[(Head@fieldObject[["indices",1]])]==ToString[derField],
If[(Length@firstDerivative)>0,
deltaIndices = {(List@@(fieldObject[["indices",1]]))[[1]]-> (List@@firstDerivative)};
,
deltaIndices = {((fieldObject[["indices",1]]))-> (firstDerivative)};
];
If[#==1,
prefactors = {};
,
prefactors = Flatten[Outer[Join,oneActionTerm[[2+1;;2+#-1,"indices"]],{{firstDerivative}},1],1];
];
newfullPrefactor = startingPrefactor;
newfullPrefactor[[2]] =Join[startingPrefactor[[2]],prefactors];
Join[{newfullPrefactor},oneActionTerm[[2;;2+#-1]],oneActionTerm[[2+#+1;;-1]]]/.deltaIndices/.derField[{dummyaaa___}]-> derField[dummyaaa]
,
Nothing
]
)&/@Range[Length@oneActionTerm[[3;;-1]]];(*bc first entry is pref and second is S*)
Return[derAction]
]
(* ::Input::Initialization:: *)
Clear[replaceExpectationValue]
replaceExpectationValue[derAction_]:=Module[{},
replaceExpectationValue[{},derAction]
]
replaceExpectationValue[expDerAction_, derAction_] := Module[{currentTerm,restDerAction,replacedTerms,expDerActionNew},
currentTerm = derAction[[1]];
restDerAction = Drop[derAction,1];
replacedTerms = replaceOneExpectationValue[currentTerm];
expDerActionNew = Join[expDerAction,replacedTerms];
replaceExpectationValue[expDerActionNew,restDerAction]
]
replaceExpectationValue[expDerAction_, {}] := Module[{},
Return[expDerAction]
]
(* ::Input::Initialization:: *)
Clear[replaceOneExpectationValue]
replaceOneExpectationValue[ActionTerm_]:=Module[{newActionTerms},
newActionTerms = scanForFirstClassicalFieldAndReplace[ActionTerm];
replaceOneExpectationValue[{},newActionTerms]
]
replaceOneExpectationValue[replacedActionTerms_, ActionTerm_] := Module[{currentActionTerm ,restActionTerm,newActionTerms,replacedActionTermsNew,restActionTermNew},
currentActionTerm = ActionTerm[[1]];
restActionTerm = Drop[ActionTerm,1];
newActionTerms = scanForFirstClassicalFieldAndReplace[currentActionTerm];
If[newActionTerms == currentActionTerm,
replacedActionTermsNew = Join[replacedActionTerms,{newActionTerms}];
restActionTermNew = restActionTerm;
,
restActionTermNew = Join[newActionTerms,restActionTerm];
replacedActionTermsNew = replacedActionTerms;
];
replaceOneExpectationValue[replacedActionTermsNew,restActionTermNew]
]
replaceOneExpectationValue[expDerAction_, {}] := Module[{},
Return[expDerAction]
]
(* ::Input::Initialization:: *)
Clear[scanForFirstClassicalFieldAndReplace]
scanForFirstClassicalFieldAndReplace[ActionTerm_]:=Module[{iter, positionFirstClField,newActionTerms,dummyIndex, newExpFieldObject, newPropObject, newDerObject},
positionFirstClField = 0;
For[iter = 2, iter <= Length@ActionTerm, iter++,
If[StringMatchQ[ActionTerm[[iter,"type"]],"classicalField"]==True,
positionFirstClField = iter;
iter = Length@ActionTerm;
]
];
If[positionFirstClField==0,
Return[ActionTerm]
,
newExpFieldObject = ActionTerm[[positionFirstClField]];
newExpFieldObject[["type"]] = "Field";
dummyIndex = Unique[Global`a83];
newPropObject = ActionTerm[[positionFirstClField]];
newPropObject[["type"]] = "Propagator";
newPropObject[["indices"]] = Join[ActionTerm[[positionFirstClField,"indices"]],{dummyIndex}];
newDerObject =ActionTerm[[positionFirstClField]];
newDerObject[["type"]] = "DerField";
newDerObject[["indices"]] = {dummyIndex};
newActionTerms = {Join[ActionTerm[[1;;positionFirstClField-1]],{newExpFieldObject},ActionTerm[[positionFirstClField+1;;-1]]],Join[ActionTerm[[1;;positionFirstClField-1]],{newPropObject,newDerObject},ActionTerm[[positionFirstClField+1;;-1]]]};
Return[newActionTerms]
]
]
(* ::Input::Initialization:: *)
Clear[takeFinalFieldDerivatives]
takeFinalFieldDerivatives[ActionTerms_]:=Module[{},
takeFinalFieldDerivatives[{},ActionTerms]
]
takeFinalFieldDerivatives[DerActionTerms_, ActionTerms_] := Module[{currentActionTerm,DerActionTermsNew,ActionTermsNew,newDerTerm,ActionTermsNewAll},
currentActionTerm = ActionTerms[[1]];
ActionTermsNew = Drop[ActionTerms,1];
newDerTerm = takeOneFinalFieldDerivative[currentActionTerm];
Switch[newDerTerm ,
{},DerActionTermsNew = Join[DerActionTerms,newDerTerm];
ActionTermsNewAll = ActionTermsNew;
,
{currentActionTerm},DerActionTermsNew = Join[DerActionTerms,newDerTerm];
ActionTermsNewAll = ActionTermsNew;
,
_,
ActionTermsNewAll = Join[newDerTerm,ActionTermsNew];
DerActionTermsNew = DerActionTerms;
];
takeFinalFieldDerivatives[DerActionTermsNew,ActionTermsNewAll]
]
takeFinalFieldDerivatives[DerActionTerms_, {}] := Module[{},
Return[DerActionTerms]
]
(* ::Input::Initialization:: *)
Clear[takeOneFinalFieldDerivative]
takeOneFinalFieldDerivative[ActionTerm_]:=Module[{newActionTerms},
newActionTerms = scanForLastDerAndReplace[ActionTerm];
takeOneFinalFieldDerivative[{},newActionTerms]
]
takeOneFinalFieldDerivative[replacedActionTerms_, ActionTerm_] := Module[{currentActionTerm ,restActionTerm,newActionTerms,replacedActionTermsNew},
currentActionTerm = ActionTerm[[1]];
restActionTerm = Drop[ActionTerm,1];
newActionTerms = scanForLastDerAndReplace[currentActionTerm];
If[newActionTerms == {currentActionTerm},
replacedActionTermsNew = Join[replacedActionTerms,newActionTerms];
,
restActionTerm = Join[newActionTerms,restActionTerm];
replacedActionTermsNew = replacedActionTerms;
];
takeOneFinalFieldDerivative[replacedActionTermsNew,restActionTerm]
]
takeOneFinalFieldDerivative[expDerAction_, {}] := Module[{},
Return[expDerAction]
]
(* ::Input::Initialization:: *)
Clear[scanForLastDerAndReplace]
scanForLastDerAndReplace[ActionTerm_]:=Module[{iter, positionLastDer,newActionTerms,dummyIndex, newExpFieldObject, newPropObject, newDerObject},
positionLastDer = 0;
For[iter = Length@ActionTerm, iter >= 2, iter--,
If[StringMatchQ[ActionTerm[[iter,"type"]],"DerField"]==True,
positionLastDer = iter;
iter = 2;
]
];
Switch[positionLastDer,
0,
Return[{ActionTerm}],
Length@ActionTerm,
Return[{Nothing}],
_,
newActionTerms = takeRightDer[ActionTerm,positionLastDer];
Return[newActionTerms]
]
]
(* ::Input::Initialization:: *)
(* I have no idea if these prefactors are correct or consistent with the rest*)
Clear[takeRightDer]
takeRightDer[ActionTerm_,positionLastDer_]:=Module[{positionFields,newOneActionTerm,newActionTerms,iter,replacementrules,dummyIndexProp1,dummyIndexProp2},
positionFields = (Switch[ActionTerm[[#,"type"]],
"Field",{#,"Field"},
"Propagator",{#,"Propagator"},
"nPoint",If[ActionTerm[[#,"spec"]]=="none",{#,"nPoint"}]
])&/@Range[Length@ActionTerm,positionLastDer+1,-1];
newActionTerms = (
iter = positionFields[[#,1]];
Switch[positionFields[[#,2]],
"Field",
newOneActionTerm = Join[ActionTerm[[1;;positionLastDer-1]],ActionTerm[[positionLastDer+1;;iter-1]],ActionTerm[[iter+1;;-1]]];
newOneActionTerm[[1,2]] = Join[ActionTerm[[1,2]],Tuples[{ActionTerm[[positionLastDer,"indices"]],ActionTerm[[positionLastDer+1;;iter-1,"indices"]]}]];
replacementrules = {ActionTerm[[positionLastDer,"indices",1]]-> ActionTerm[[iter,"indices",1]]};
newOneActionTerm =newOneActionTerm/.replacementrules;
,
"Propagator",
dummyIndexProp1 = Unique[Global`a83];
dummyIndexProp2 = Unique[Global`a83];
newOneActionTerm = Join[ActionTerm[[1;;positionLastDer-1]],ActionTerm[[positionLastDer+1;;iter-1]],{<|"type"->"Propagator","indices"->{ActionTerm[[iter,"indices",1]],dummyIndexProp1}|>,<|"type"->"nPoint","indices"->{dummyIndexProp1,ActionTerm[[positionLastDer,"indices",1]],dummyIndexProp2},"nPoint"->3,"spec"->"none"|>,<|"type"->"Propagator","indices"->{dummyIndexProp2,ActionTerm[[iter,"indices",2]]}|>},ActionTerm[[iter+1;;-1]]];
newOneActionTerm[[1,2]] = Join[ActionTerm[[1,2]],{-1}, {{dummyIndexProp2,dummyIndexProp2}},Tuples[{ActionTerm[[positionLastDer,"indices"]],Join[ActionTerm[[positionLastDer+1;;iter-1,"indices"]],{ActionTerm[[iter,"indices",1]]}]}]];
,
"nPoint",
newOneActionTerm = ActionTerm;
newOneActionTerm[[iter,"nPoint"]] = ActionTerm[[iter,"nPoint"]]+1;
newOneActionTerm[[iter,"indices"]] = Join[ActionTerm[[iter,"indices",1]],ActionTerm[[positionLastDer,"indices",1]],ActionTerm[[iter,"indices",2;;-1]]];
newOneActionTerm[[1,2]] = Join[ActionTerm[[1,2]], {{ActionTerm[[positionLastDer,"indices",1]],ActionTerm[[iter,"indices",1]]}}];
newOneActionTerm = Drop[newOneActionTerm,positionLastDer];
];
newOneActionTerm
)&/@Range[Length@positionFields];
Return[newActionTerms]
]
(* ::Input::Initialization:: *)
Clear[DerRules] (* works for regs, regdots, props, nPoints, fields *)
DerRules[operator_,dummyFieldIndex_] := Module[{operatorType,firstDummyProp, secondDummyProp,dummynPoint,operatorDer,firstDummyIndices,secondDummyIndices, operatorPref,indexReplacement = {}},
myEcho["DerRules",1];
myEcho[{"operator: ",operator},2];
operatorType = operator[["type"]];
myEcho[{"operator type: ", operatorType},3];
firstDummyIndices = Unique[Global`a83];
secondDummyIndices = Unique[Global`a83];
Switch[operatorType,
"Regulator",
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
myEcho["Regulator Der",2];
myEcho[{operatorPref,operatorDer},3];,
"Regulatordot",
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
myEcho["Regulatordot Der",2];
myEcho[{operatorPref,operatorDer},3];,
"Propagator",
firstDummyProp = operator;
firstDummyProp[["indices",2]]=firstDummyIndices;
secondDummyProp = operator;
secondDummyProp[["indices",1]]=secondDummyIndices;
dummynPoint = <|"type"-> "nPoint", "indices"-> Table[Null,3], "nPoint"-> 3, "spec"-> "none"|>;
dummynPoint[["indices"]][[1]]=firstDummyIndices;
dummynPoint[["indices"]][[2]]=dummyFieldIndex;
dummynPoint[["indices"]][[3]]=secondDummyIndices;
operatorDer = {firstDummyProp,dummynPoint,secondDummyProp};
operatorPref = {-1,{operator[["indices",1]],dummyFieldIndex},{secondDummyIndices,secondDummyIndices}};
myEcho["Propagator Der",2];
myEcho[{operatorPref,operatorDer},3]; ,
"nPoint",
Switch[operator[["spec"]],
"none",
dummynPoint = operator;
dummynPoint[["nPoint"]] = operator[["nPoint"]]+1;
dummynPoint[["indices"]] = Table[Null,operator[["nPoint"]]+1];
dummynPoint[["indices",1]] = operator[["indices",1]];
dummynPoint[["indices",2]] = dummyFieldIndex;
(dummynPoint[["indices",#]] = operator[["indices",#-1]])&/@Table[i,{i,3,dummynPoint[["nPoint"]]}];
operatorDer = {dummynPoint};
operatorPref = {{dummynPoint[["indices",1]],dummyFieldIndex}};
myEcho["nPoint Der",2];
myEcho[{operatorPref,operatorDer},3];,
"BRST",
dummynPoint = operator;
dummynPoint[["nPoint"]] = operator[["nPoint"]]+1;
dummynPoint[["indices"]] = Table[Null,operator[["nPoint"]]+1];
dummynPoint[["indices",1]] = operator[["indices",1]];
dummynPoint[["indices",2]] = dummyFieldIndex;
(dummynPoint[["indices",#]] = operator[["indices",#-1]])&/@Table[i,{i,3,dummynPoint[["nPoint"]]}];
operatorDer = {dummynPoint};
operatorPref = {{dummynPoint[["indices",1]],dummyFieldIndex}};
myEcho["nPoint Der",2];
myEcho[{operatorPref,operatorDer},3];,
"classical",
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
];
,
"Field",
If[Length@dummyFieldIndex>0,
If[ToString[Head[operator[["indices",1]]]]==ToString[Head[dummyFieldIndex]],
operatorDer = {};
operatorPref = {1};
indexReplacement = {operator[["indices",1]]-> dummyFieldIndex};
,
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
];
,
If[ToString[Head[operator[["indices",1]]]]==ToString[dummyFieldIndex],
operatorDer = {};
operatorPref = {1};
indexReplacement = {operator[["indices",1]]-> dummyFieldIndex};
,
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
];
];
,
_,
operatorDer = {{"dummyEntry"}};
operatorPref = {0};
myEcho["no Der defined for this object",2];
];
Return[{operatorPref,operatorDer,indexReplacement}]
]
(* ::Input::Initialization:: *)
Clear[MatchDerIndices]
MatchDerIndices[field_,dummyindex_] := Module[{replacementList},
myEcho["MatchDerIndices",2];
replacementList = {dummyindex->field};
Return[replacementList]
]
(* ::Input::Initialization:: *)
Clear[MultiplyFactorsFuncDer]
MultiplyFactorsFuncDer[prefList_] := Module[{product = 1, metricfactors = {}},
myEcho[{"prefactor: ",prefList},3];
(Switch[Head[prefList[[#]]],
Integer, product = product* prefList[[#]];,
Rational, product = product* prefList[[#]];,
List, metricfactors = Join[metricfactors,{prefList[[#]]}];
])&/@Table[i,{i,1,Length@prefList}];
myEcho[{"multiplied prefactor: ",Join[{product},metricfactors]},3];
Return[Join[{product},metricfactors]]
]
(* ::Input::Initialization:: *)
Clear[FuncDer]
FuncDer[RHS_,field_] := Module[{dummyFieldIndex,AllDerivatives, FirstIndices, SecondIndices, ThirdIndices, dummyEntry, elements, elementsPref, PreviousPref, ThreePoint, SecondProp, nPoint, nP, ProductRuleNumber, RHSdummy = RHS,operatorPref,operatorDer,replacementList,indexReplacement2},
myEcho["FuncDer",1];
myEcho[{"Equation: ", RHS},2];
dummyFieldIndex = (*Unique[Global`iext]*)field;
AllDerivatives = Table[Null,Length@RHSdummy-1]; (*All Derivatives has the length of all Props/nPoints in the RHS expression*)
(*PreviousPref: This gives the (-1)^(field,field) factors in the prefactor from the permutation of fields in the derivative product rule*)
PreviousPref = Join[{{}},{{1}},Table[Null,Length@RHSdummy-2]];
(*change this according to the starting point which was figured out below*)
(If[RHSdummy[[#-1]][["type"]] =="Regulator"||RHSdummy[[#-1]][["type"]] =="Regulatordot"||(RHSdummy[[#-1]][["type"]] =="nPoint"&& RHSdummy[[#-1]][["spec"]] =="classical"),
PreviousPref[[#]] = PreviousPref[[#-1]];
,
PreviousPref[[#]] = Join[PreviousPref[[#-1]], Tuples[{RHSdummy[[#-1]][["indices"]],{dummyFieldIndex}}]];
])&/@Table[i,{i,3,Length@RHS}];
(*Check for each master equation entry if prop or nPoint and find derivative of the object*)
(ProductRuleNumber = #;
myEcho[{"Product Rule No.: ", #},3];
{operatorPref,operatorDer,indexReplacement2} = DerRules[RHSdummy[[#]],dummyFieldIndex];
RHSdummy[[1,2]] = Join[RHS[[1,2]],operatorPref];
RHSdummy[[#]] = operatorDer;
RHSdummy = Join[{RHSdummy[[1]]},Flatten@RHSdummy[[2;;Length@RHSdummy]]];
If[Length@indexReplacement2>0,
RHSdummy = RHSdummy/.indexReplacement2;
];
If[MemberQ[{RHSdummy},{{"dummyEntry"}}],
Nothing,
RHSdummy[[1,2]] = Sort[Join[RHSdummy[[1,2]],PreviousPref[[#]]]];
];
AllDerivatives[[ProductRuleNumber-1]] = RHSdummy;
RHSdummy = RHS;
)&/@Table[i,{i,2,Length@RHSdummy}];
myEcho [{"All Derivatives: ",AllDerivatives},4];
replacementList = MatchDerIndices[field,dummyFieldIndex];
AllDerivatives = AllDerivatives/.{stuff___,"dummyEntry",furtherstuff___}->Nothing;
(AllDerivatives[[#,1,2]] = MultiplyFactorsFuncDer[AllDerivatives[[#,1,2]]])&/@Table[i,{i,1,Length@AllDerivatives}];
Return[{AllDerivatives, replacementList}]
]
(* ::Input::Initialization:: *)
Clear[MultipleFuncDer]
(*MultipleFuncDer[RHSlist_,fieldlist_] := Module[{truefieldlist, indexOptions},
indexOptions = fieldlist[["IndexStructure"]];
truefieldlist =fieldlist[["FieldDerivatives"]];
MultipleFuncDer[RHSlist,truefieldlist, {},indexOptions]
]*)
MultipleFuncDer[RHSlist_,fieldlist_] := MultipleFuncDer[RHSlist,fieldlist,{}]
MultipleFuncDer[RHSlist_,fieldlist_,replacementList_] := Module[{dummysuperindexlist,firstfield, newfieldlist, newRHSlist,newreplacementList,intResult},
myEcho["MultipleFuncDer",1];
firstfield = Last@fieldlist; (*replaced first with last and 1 with -1 to get correct order of derivatives*)
newfieldlist = Drop[fieldlist,-1];
(*check if its still the master eq or already a list of list of func ders*)
If[MemberQ[{RHSlist[[1]]}, "Prefactor"-> {__}],
myEcho["First FuncDer",2];
{newRHSlist,newreplacementList} = FuncDer[RHSlist,firstfield];
,
myEcho["Further FuncDer",2];
newRHSlist =Table[Null,{i,1,Length@RHSlist}];
newreplacementList= Table[Null,{i,1,Length@RHSlist}];
intResult=ParallelMap[(FuncDer[RHSlist[[#]],firstfield])&,Table[i,{i,1,Length@RHSlist}]];
({newRHSlist[[#]],newreplacementList[[#]]} = intResult[[#]])&/@Table[i,{i,1,Length@RHSlist}];
newRHSlist = Flatten[newRHSlist,1];
];
newreplacementList = Flatten@Join[replacementList, newreplacementList];
MultipleFuncDer[newRHSlist,newfieldlist,newreplacementList]
]
MultipleFuncDer[RHSlist_,{},newreplacementList_] := Module[{finalRHSlist},
finalRHSlist = (If[StringContainsQ[ToString[RHSlist[[#]]],"Field"],
Nothing,
RHSlist[[#]]
])&/@Range[Length@RHSlist];
Return[{finalRHSlist,newreplacementList}]
]
(* ::Input::Initialization:: *)
IndexProjection[iii_,jjj_] := Module[{},Return[iii->jjj]]
(* ::Input::Initialization:: *)
Clear[GetFieldsList]
GetFieldsList[fields_] := Module[{keys,bosons, fermions, BRSTs, BRSTbosons, BRSTfermions,fullList},
myEcho["GetFieldsList",1];
keys = Keys[fields];
If[MemberQ[keys,"bosonic"] == True,
bosons = Map[Head,fields[["bosonic"]]];
,
bosons = {};
];
If[MemberQ[keys,"fermionic"] == True,
fermions = Map[Head,fields[["fermionic"]],{2}];
,
fermions = {};
];
If[MemberQ[keys,"BRSTsources"]== True,
(Switch[fields[["BRSTsources",#,2]],
"bosonic",
bosons = Join[bosons,{fields[["BRSTsources",#,1]]}];,
"fermionic",
fermions = Join[fermions,{fields[["BRSTsources",#,1]]}];
]
)&/@Range[Length@fields[["BRSTsources"]]];
,
Nothing
];
fullList = {bosons,fermions};
Return[fullList]
]
(* ::Input::Initialization:: *)
(*define the possible propagators for fields*) (*Adjust such that one can insert a truncation (done) and vertex ordering...*)
Clear[getPossibleProps]
getPossibleProps[fields_,truncation___]:= Module[{keys,bosonicfields,testbosonicfield, fermionicfields,PossibleProps = {},TruncatedPossibleProps = {}, PossibleBosonProps, PossibleFermionProps},
myEcho["GetPossibleProps",1];
keys = Keys[fields];
If[MemberQ[keys,"bosonic"] == True,
bosonicfields = Map[Head,fields[["bosonic"]]];
,
bosonicfields = {};
];
If[MemberQ[keys,"fermionic"] == True,
fermionicfields = Map[Head,fields[["fermionic"]],{2}];
,
fermionicfields = {};
];
PossibleBosonProps = Permutations[Join[bosonicfields,bosonicfields],{2}];
myEcho[{"Possible Boson Props",PossibleBosonProps},3];
PossibleFermionProps = Join[Tuples[{fermionicfields[[All,1]],fermionicfields[[All,2]]}],Map[Reverse,Tuples[{fermionicfields[[All,1]],fermionicfields[[All,2]]}],1]];
myEcho[{"Possible Fermion Props",PossibleFermionProps},3];
PossibleProps = Join[PossibleBosonProps,PossibleFermionProps];
(* if a Truncation is specified, the other props are removed *)
(* !!!!!!!!!!!!!!!!!!!!! does this still work?????!!!!!!!*)
If[Length@truncation>0,
myEcho["Truncate possible props",3];
(If[MemberQ[truncation,{OrderlessPatternSequence[PossibleProps[[#,1]],PossibleProps[[#,2]]]}],
TruncatedPossibleProps = Join[TruncatedPossibleProps,{PossibleProps[[#]]}];
,
Nothing
])&/@Range[Length@PossibleProps];
PossibleProps = TruncatedPossibleProps;
myEcho[{"poss props",PossibleProps},3];
,
Nothing
];
Return[PossibleProps];
]
(* ::Input::Initialization:: *)
(* get an assoc with the positions of objects *)
Clear[getAllObjectPositionsSuperindex]
getAllObjectPositionsSuperindex[RHSDiagram_]:= Module[{props ,regs, vertices, classical, brst,positionAssoc},
props = regs = vertices = classical= brst = {};
(Switch[RHSDiagram[[#,"type"]],
"Propagator",props =Join[props,{#}];,
"Regulator",regs=Join[regs,{#}];,
"Regulatordot",regs=Join[regs,{#}];,
"nPoint",
Switch[RHSDiagram[[#,"spec"]],
"none",vertices= Join[vertices,{#}];,
"classical",classical=Join[classical,{#}];,
"BRST", brst=Join[brst,{#}];
];
])&/@Range[2,Length@RHSDiagram,1];
positionAssoc = <|"Propagators" -> props, "Regulators" -> regs, "classicalVertices"-> classical,"BRSTVertices"-> brst, "Vertices"-> vertices|>;
Return[positionAssoc]
]
(* ::Input::Initialization:: *)
(*get possible index configs for props and regs*)
Clear[getObjectIndexMapping]
getObjectIndexMapping[diagram_,objectPositionAssoc_,Truncation_,indexConfigs_,objectType_,allfields_]:= Module[{objectSuperindices,possibleSets,allConfigs,appliedObjectSuperindices,fieldHeads,allConfigsnew,allIndexConfigs},
myEcho["getObjectIndexMapping",1];
(* get all object superindices *)
objectSuperindices = ((diagram[[#,"indices"]])&/@objectPositionAssoc[[objectType]]);
(* map superindices onto possible configs *)
If[Length@objectPositionAssoc[["Propagators"]]>0,
If[Length@objectSuperindices>0,
(* hard sum over all prop and reg configs and remove impossible ones *)
If[(objectType == "Regulators" ||objectType == "Propagators"),
allConfigs = getAllPossibleSets[objectSuperindices,Truncation];
(* apply previous index configs and remove impossible configs & check if one object index is already field and modify all Configs accordingly*)
If[allConfigs=={},
allIndexConfigs= {"Null"};
,
If[Length@indexConfigs>0,
appliedObjectSuperindices = objectSuperindices/.indexConfigs;
allIndexConfigs = Flatten[(checkHeads[appliedObjectSuperindices[[#]],objectSuperindices,allConfigs,indexConfigs[[#]],allfields])&/@Range[Length@indexConfigs],1];
,
allIndexConfigs = checkHeads[objectSuperindices,objectSuperindices,allConfigs,indexConfigs,allfields];
];
If[allIndexConfigs == {},
allIndexConfigs= {"Null"};
];
(*,
allIndexConfigs = indexConfigs;*)
];
,
(* after fixing the prop and reg indices, the vertex indices are automatically set and only need to be compared to the truncation *)
allConfigs = getPossibleVertexList[Truncation];
If[allConfigs=={},
allIndexConfigs= {"Null"};
,
appliedObjectSuperindices = objectSuperindices/.indexConfigs;
(* go through different vertex configs and then through each vertex *)
allIndexConfigs = ((compareAllVertexHeads[appliedObjectSuperindices[[#]],allConfigs,indexConfigs[[#]],allfields])&/@Range[Length@indexConfigs])/.{"Null"}->Nothing;