FunctionalDiagrams · map of the public functions

132 public names, 548 dependencies (version 2.4.0). Point at a name, or tab to it, to see what it uses (lines in the colour of the name used, darker towards it) and what uses it (dashed); click, tap or press Enter to keep the selection, Escape or a click on the background to release it.

The 132 public names of the package in 13 groups, and the 548 dependencies between them, by their role in a calculation: 1 declare the symbols, 2 write a functional, 3 differentiate it (FunctionalDerivative, the hub, with the names built on it), then 4 classify and check, 5 draw and 6 evaluate the diagrams. A name indented under another is built on it; "uses" lists the other names it uses (version 2.4.0).FunctionalDiagrams·map of the public functions132 public names · 548 dependenciesYou write a functional (Z, W = log Z, an effective action, Φ): its functional derivatives are the diagrams.The others declare the symbols and classify, draw and evaluate the diagrams: all 132 public names, by their role.1Declarefields, sources, propagators, couplingsDeclareSourceDeclareGrassmannSourceDeclareGrassmannOddDeclareFieldDeclareGrassmannGradedDeclareBlobDeclareSymmetricDeclareAntisymmetricDeclareFunctionalDerivativeDeclareDiscreteIndexValuesDeclareLineStyleDeclareInteractionLineDeclareDirectedPropagatorDeclareCouplingDeclareDisplayNameDeclareLocalVertexResetDeclarations2Write a functionalZ₀ and the interaction, in the notation of the packageZ0 = Exp[-IntegralOver[G0[x, y] etabar[x] ** eta[y], {x, y}]]then W = log Z, Γ (1PI, 2PI), Φ: see stage 3NOTATION· read by 54 of the 95 functionsIntegralOver49DeltaFunction50GrassmannProduct49DummyVariable48TRACES, LEGENDRE TRANSFORMSTraceLogOperatorTraceOperatorKernelLegendreTransformLegendrePropagatorAUXILIARY FIELDSHubbardStratonovichusesSimplifyDiagrams,LabelFunctionIntegrateOutFieldusesSetSourcesToZero,LabelFunction3DifferentiateCalculusPerturbation theoryFunctionals and verticesChannels and the parquetTree expansionEffective actions and operator tracesδFunctionalDerivativeof Z and W: correlation functionsof Γ: vertex functionsof Φ: Σ and Γ⁰SimplifyDiagramsthe canonical formOrderPartthe orders keptSetSourcesToZeroFieldExpectationValueusesFieldDerivativeFieldDerivativePerturbativeCorrelationFunctionusesDropVacuumBubblesLuttingerWardFunctionalusesConnectedDiagramsEffectiveAction2PIGaussianExpectationValueConnectedCorrelationFunctionusesConnectedDiagramsPerturbativeFullVertexPerturbativeDensityVertexusesSkeletonDiagrams,AmputateExternalLegsSelfEnergyIrreducibleVertexConnectedVacuumDiagramsusesConnectedDiagramsConnectedFunctionFromVerticesusesDiagramTermsFullPropagatorVertexFunctionMeanFieldExternalSourceEffectiveAction1PISuperfieldComponentsusesExpandTracealso in this stageDiagramTermsExpandTraceSelfEnergyFunctional4Classify and checkDIAGRAM CLASSESClosedLoopCountZeroDimensionalValueusesDiagramTermsConnectedDiagramsDropVacuumBubblesParticleIrreducibleQParticleIrreducibleDiagramsSkeletonDiagramsDropClosedLoopsAmputateExternalLegsCHANNELS AND THE PARQUETBetheSalpeterLadderusesSimplifyDiagramsExactEquationusesOrderPartCheckParquetEquationsusesSimplifyDiagramsDysonSeriesusesSimplifyDiagramsTwoParticleReducibleQReducibleDiagramsIrreducibleDiagramsParquetDecompositionLabelFunctionCheckEquation5DrawPICTURESDiagramPlotDrawDiagramExpressionToLaTeXusesBubbleIntegralDiagramToTikZHow to read the mapFunctiona function, in its group’s colourHeadan inert head, used as dataABusesCB is built on Aand also uses C“uses” leaves out the names of 1 and 2 and theinert heads, read by many functions; theinteractive map has every dependency.6EvaluateMATSUBARA SUMSDiagramIntegrand → MatsubaraSum →AnalyticContinuationDeclareMatsubaraFrequencyMatsubaraSumDiagramIntegrandEvaluateMatsubaraAnalyticContinuationCheckCuttingRulesusesRetardedImaginaryPartRetardedImaginaryPartCuttingRuleImaginaryPartZeroTemperatureLimitFermiFunctionBoseFunctionLoopMomentumLoopFrequencyMomentumSumEnergyDeltaTemperatureDIMENSIONAL REGULARIZATIONDiagramLoopIntegralGFunctionBubbleIntegralusesTadpoleIntegralIntegrateLoopsEpsilonExpandPolePartInfraredRearrangedIntegralTadpoleIntegralMassInsertionusesSimplifyDiagramsBetaFunctionFromZAnomalousDimensionFromZScalarPropagatorMomentumSquaredRenormalizationScaleLoopIntegralFeynmanParameterIntegralFeynmanParameterQED AT ONE LOOPDiracSimplifyDiracOrderIntegrateOneLoopVertexFormFactorsQEDIntegrandCombineParameterIntegralsReduceParameterIntegralsExpandParameterIntegralsusesEpsilonExpandDifferentiateUnderIntegralGammaMatrixSlashedMomentumDiracProductDiracTraceSpinorChainLorentzMetricFourVectorScalarProductSpacetimeDimensionSimplexIntegralFeynmanDenominatorParameterIntegralMinkowskiLoopIntegral