FeynCalc is a Mathematica package for algebraic calculations in
Quantum Field Theory and semi-automatic evaluation of Feynman
Diagrams.
Tutorials
Basic objects
- Abbreviation - gives a shortname
for name (in
HoldForm)
- AntiQuarkField, QuarkField, QuarkFieldPsi, QuarkFieldPsiDagger, QuarkFieldChi, QuarkFieldChiDagger - name of a
fermionic field
- CA, CF - Casimir
operator eigenvalues of SU(N)
- CGA, CGS, CGAD, CGSD, CGAE, CGSE -
representation of Dirac matrices with Cartesian indices or Dirac
matrices contracted to 3-momenta
- CSI, CSID, CSIE, CSIS, CSISD, CSISE -
Pauli matrices with Cartesian indices or Pauli matrices contracted to
3-momenta
- CSP, CSPD, CSPE - scalar products of 3-momenta
- CV, CVD, CVE - Cartesian 3-vectors
- CartesianIndex - Cartesian
index
- CartesianMomentum - internal
representation of 3-momenta
- CartesianPair - special pairing
used in the internal representation to represent Kronecker deltas, 3-vectors or Cartesian scalar products
- DiracBasis - can be used as a
separator in the SPVAT-decomposition
- DeltaFunction, DeltaFunctionPrime, DeltaFunctionDoublePrime -
Dirac delta function and its derivatives
- DiracGamma, GA, GA5, GS, GAD, GSD, GAE, GSE - Dirac matrices and Feynman slashes
- GALP, GALN, GALR, GALPD, GALND, GALRD, GSLP, GSLN, GSLR, GSLPD, GSLND, GSLRD -
Lightcone components of Dirac matrices and Feynman slashes
- DiracIndexDelta, DIDelta - Kronecker delta in the Dirac
space
- DiracSigma - denotes \frac{i}{2}[\gamma^\mu, \gamma^\nu]
- DOT - noncommutative multiplication
sign
- Eps, LC, LCD, CLC, CLCD - totally antisymmetric \varepsilon (Levi-Civita) tensor
- EpsilonUV, EpsilonIR, Epsilon - \varepsilon from dimensional
regularization
- ExplicitLorentzIndex, LorentzIndex - Lorentz index
- ExplicitDiracIndex, DiracIndex - Dirac index
- ExplicitPauliIndex, PauliIndex - Pauli index
- ExplicitSUNIndex, SUNIndex - SU(N) adjoint index
- ExplicitSUNFIndex, SUNFIndex - SU(N) fundamental index
- FAD, SFAD, CFAD, GFAD, FeynAmpDenominator - denominators
of Feynman amplitudes
- FCGV - a global variable
- FCIteratedIntegral - Chen’s
iterated integral
- FCHPL, FCGPL
- harmonic and Goncharov polylogarithms
- FCPartialFractionForm -
partial fractioned form of rational functions
- FCTensor, FCVariable, FreeIndex, GrassmannParity, ImplicitDiracIndex, ImplicitPauliIndex, ImplicitSUNFIndex, NegativeInteger, NonCommutative, PositiveInteger, PositiveNumber - various
datatypes
- FUNCTION - declaration of functions
for Write2
- DCHN, DiracChain - Dirac chain with explicit
open Dirac indices
- FeynAmp, FeynAmpList - Feynman amplitudes
- FCPartialD, LeftNablaD, LeftRightNablaD, LeftRightNablaD2, LeftPartialD, LeftRightPartialD, LeftRightPartialD2, RightNablaD, RightPartialD - partial derivatives
acting on operators
- FCTopology - representation of a
loop integral family topology
- FV, FVD, FVE - Minkowskian 4-vectors
- FVLP, FVLN, FVLR, FVLPD, FVLND, FVLRD -
Lightcone components of Minkowskian 4-vectors
- GaugeField - name of a gauge
field
- GaugeXi - gauge parameter \xi
- GluonField - name of a gluon
field
- IFPD - denotes p^2 - m^2
- KD, KDD, KDE - Cartesian Kronecker delta \delta^{ij}
- Li2, Li3, Li4 - polylogarithms of different weights
- LightConePerpendicularComponent
- internal representation for perpendicular components of 4-momenta and Lorentz indices
- Momentum - internal representation of
4-momenta
- MT, MTD, MTE - metric tensor g^{\mu \nu}
- MTLP, MTLN, MTLR, MTLPD, MTLND, MTLRD -
Lightcone components of the metric tensor g^{\mu \nu}
- Nf - number of flavors n_f
- Pair - special pairing used in the
internal representation to represent the metric, scalar products or
4-vectors
- PCHN, PauliChain - Pauli chain with explicit
open Pauli indices
- PauliEta, PauliXi - Pauli spinors
- PauliIndexDelta, PIDelta - Kronecker delta in the Pauli
space
- PauliSigma - internal
representation of Pauli matrices
- Polarization - internal
representation of polarizations
- PolarizationVector -
polarization vector
- PlusDistribution - a special
distribution
- PropagatorDenominator,
PD, StandardPropagatorDenominator,
CartesianPropagatorDenominator,
GenericPropagatorDenominator
- internal representation of propagator denominators
- QuantumField - generic name of a
quantum field
- ScaleMu - \mu scale in dimensional regularization
- SD, SUNDelta
- Kronecker delta for adjoint SU(N)
indices
- SDF, SUNFDelta - Kronecker delta for fundamental
SU(N) indices
- SI, SID, SIE, SIS, SISD, SISE - Pauli
matrices with Lorentz indices or Pauli matrices contracted to 4-momenta
- SmallDelta, SmallEpsilon - some small positive
numbers
- SmallVariable - small variable
to be used as a regulator in Passarino-Veltman functions
- Spinor, SpinorU, SpinorUBar, SpinorV, SpinorVBar, SpinorUD, SpinorUBarD, SpinorVD, SpinorVBarD - Dirac spinors
- SP, SPD, SPE - scalar products of 4-momenta
- SPLP, SPLN, SPLR, SPLPD, SPLND, SPLRD -
Lightcone components of Mikowskian scalar products
- StandardMatrixElement -
special head for isolating Dirac and color structures from the rest of
the expression
- SUND - structure constant d^{abc} in SU(N)
- SUNF - structure constant f^{abc} in SU(N)
- SUNN - n_c in SU(N)
- SUNT, SUNTF -
T^a_{ij} of SU(N) in the fundamental representation
- TC - temporal component of a 4-vector, i.e. p^0
- TGA - temporal component of a Dirac
matrix, i.e. \gamma^0
- TemporalMomentum - internal
representation of temporal components of 4-momenta
- TemporalPair - special pairing
used in the internal representation to represent temporal components of
4-vectors
- Tf - T_F
group constant of SU(N)
- Zeta2, Zeta4, Zeta6, Zeta8, Zeta10 -
Riemann zeta functions \zeta_{2k} of
different even weights
Basic functions
- Apart1, Apart3 - alternative to Mathematica’s
Apart
- Cases2 - alternative to Mathematica’s
Cases
- Coefficient2 - alternative to
Mathematica’s
Coefficient
- Combine - alternative to Mathematica’s
Together
- Complement1 - alternative to
Mathematica’s
Complement
- Collect2, Collect3 - alternatives to Mathematica’s
Collect
- DataType - defines data types
- Expand2 - alternative to Mathematica’s
Expand
- ExpandAll2 - alternative to
Mathematica’s
ExpandAll
- Explicit - inserts explicit
expressions for certain objects
- Factor1, Factor2, Factor3 - alternatives to Mathematica’s
Factor
- FactorList2 - alternative to
Mathematica’s
FactorList2
- FC - changes the output format to FeynCalcForm
- FCAbbreviate - introduces
abbreviations
- FCAntiSymmetrize -
antisymmetrizes with respect to the given variables
- FCDeclareHeader, FCPrint, FCReloadAddOns, FCReloadFunctionFromFile -
for writing or debugging new FeynCalc functions or add-ons
- FCClearCache, FCMemoryAvailable, FCShowCache, FCUseCache - cache management
- FCCheckSyntax - checks for
syntax errors in the input expressions
- FCCheckVersion - checks the
FeynCalc version
- FCCompareResults - compares
results of different calculations
- FCCompareNumbers - compares
(semi)numerical expressions
- FCDisableTraditionalFormOutput,
FCEnableTraditionalFormOutput
- turns the
TraditionalForm output off or on
- FCFactorOut - factors out the
given prefactor
- FCFilePatch - patches files using
regular expressions
- FCGetNotebookDirectory
- alternative to Mathematica’s
NotebookDirectory
- FCHighlight - highlights selected
variables
- FCE, FeynCalcExternal - converts the
expression to the external FeynCalc representation
- FCF, FeynCalcForm - changes the printed
output to an easy to read form
- FCI, FeynCalcInternal - converts the
expression to the internal FeynCalc representation
- FCMakeIndex - generates indices
from strings (useful e.g. for QGRAF input)
- FCMakeSymbols - generates lists
of symbols
- FCMatchSolve - solves for
matching coefficients and renormalization constants
- FCPatternFreeQ - checks if the
expression contains any patterns
- FCProgressBar - a simplistic
progress bar
- FCReplaceAll - alternative to
Mathematica’s
ReplaceAll
- FCReorderList - reorder elements
of a list
- FCReplaceRepeated -
alternative to Mathematica’s
ReplaceRepeated
- FCShowReferenceCard -
FeynArts cheatsheet
- FCSplit, FCProductSplit, PartitHead, SelectFree, SelectNotFree, SelectFree2, SelectNotFree2, SelectSplit - alternatives to
Mathematica’s
Select
- FCSymmetrize - symmetrizes with
respect to the given variables
- FeynCalcHowToCite - lists
relevant FeynCalc publications
- FI - changes the output format to
InputForm
- FreeQ2 - alternative to Mathematica’s
FreeQ
- FRH - alternative to Mathematica’s
ReleaseHold
- ILimit, MLimit - alternatives to Mathematica’s
Limit
- Isolate, KK -
replaces expressions by abbreviations
- Map2 - alternative to Mathematica’s
Map
- MemSet - memoization depending on the
amount of free RAM
- NTerms - alternative to Mathematica’s
Length
- NumericalFactor - gives the
overall numerical factor
- NumericQ1 - alternative to
Mathematica’s
NumericQ
- Power2 - alternative to Mathematica’s
Power
- PowerFactor, PowerSimplify, XYT - simplification of expressions with
exponents
- Series2, Series3 - alternatives to Mathematica’s
Series
- SetStandardMatrixElements -
introduces abbreviations for StandardMatrixElements
- Solve2, Solve3 - alternatives to Mathematica’s
Solve
- SumP, SumS, SumT - different summations
- TimedIntegrate - alternative to
Mathematica’s
Integrate
- ToFCPartialFractionForm, FromFCPartialFractionForm -
switching between the usual and partial fractioned form representations
for rational functions
- TBox - helps implementing typesetting
rules
- TypesettingExplicitLorentzIndex
- typesettings of explicit Lorentz indices
- $TypesettingDim4, $TypesettingDimD, $TypesettingDimE - typesetting of
tensors in 4, D and D-4
dimensions
- Variables2 - alternative to
Mathematica’s
Variables
Lorentz and Cartesian
tensors
Dirac algebra
Pauli algebra
Algebra of noncommutative
objects
SU(N) algebra
Loop integrals
- A0, A00 -
Passarino-Veltman 1-point integrals (tadpoles)
- Apart2 - partial fractions loop
integrals (only very simple cases)
- ApartFF, FCLoopCreatePartialFractioningRules
- performs partial fraction decomposition of arbitrary loop
integrals
- B0, B00, B1, B11 -
Passarino-Veltman 2-point integrals (bubbles)
- C0 - Passarino-Veltman 3-point integrals (triangles)
- CTdec, Tdec -
calculates tensor decomposition formulas for loop integrals
- D0 - Passarino-Veltman 4-point integrals (boxes)
- DB0 - derivative of B0 with respect to the external momentum
- DB1 - derivative of B1 with respect to the external momentum
- FCApart - backend of [ApartFF](ApartFF), works only
on single loop integrals
- FCClausen - Clausen’s function
- FCGramMatrix - generates the Gram
matrix from the given momenta
- FCGramDeterminant -
calculates the Gram determinant
- FCDiffEqChangeVariables, FCDiffEqSolve - handling of
differential equations
- FCHideEpsilon - substitutes
\frac{1}{\varepsilon} - \Gamma_E + \log (4
\pi) with \Delta
- FCShowEpsilon - substitutes
\Delta with \frac{1}{\varepsilon} - \Gamma_E + \log (4
\pi)
- FCIntegral - head of loop
integrals
- FCIteratedIntegralEvaluate,
FCIteratedIntegralSimplify
- manipulations of Chen’s iterated integrals
- FCFeynmanFindDivergences, FCFeynmanRegularizeDivergence,
FCFeynmanParameterJoin, FCFeynmanParametrize, FCFeynmanPrepare, FCFeynmanProjectiveQ, FCFeynmanProjectivize, FCMellinJoin - derivation and
manipulation of Feynman parameter integrals
- FCLoopAddEdgeTags, FCLoopGraphPlot, FCLoopIntegralToGraph, FCLoopPropagatorsToLineMomenta
- create and plot graphs representing loop integrals
- FCLoopAddMissingHigherOrdersWarning
- adds a warning flag to the given \epsilon-expansion
- FCLoopApplyTopologyMappings,
FCLoopCreateRuleGLIToGLI,
FCLoopFindMomentumShifts,
FCLoopFindIntegralMappings,
FCLoopFindSubtopologies,
FCLoopFindTopologies, FCLoopFindTopologyMappings,
FCLoopPakOrder, FCLoopToPakForm - loop integral
topology identification and minimization
- FCGraphCuttableQ, FCGraphFindPath - graph
manipulations
- FCLoopBasisCreateScalarProducts
- auxiliary function that generates all possible loop momenta dependent
scalar products
- FCLoopBasisFindCompletion -
suggests propagators needed to have a complete loop integral basis
- FCLoopBasisGetSize -
returns the number of propagators in a topology
- FCLoopBasisIncompleteQ
- checks if the propagators of a loop integral do not form a basis
- FCLoopBasisOverdeterminedQ
- checks if the propagators of a loop integral are linearly
dependent
- FCLoopBasisSplit - checks if
the loop integral factorizes into a product of separate integrals
- FCLoopBasisExtract -
auxiliary function that extracts the scalar products from a loop
integral
- FCLoopCanonicalize -
auxiliary function that canonicalizes free Lorentz indices of 1-loop
integrals
- FCLoopCreateRulesToGLI
- rewrites scalar products as linear combinations of GLIs with negative indices
- FCLoopEikonalPropagatorFreeQ
- checks if the integral contains eikonal propagators
- FCLoopExtract - extracts loop
integrals
- FCLoopFindSectors - returns
sectors for the given GLIs
- FCLoopFromGLI - converts GLIs into explicit integrals with FeynAmpDenominators
- FCLoopGetEtaSigns - extracts
the signs of i \eta from all
propagators
- FCLoopGetKinematicInvariants
- kinematic invariants from the given topology.
- FCLoopGLIDifferentiate
- differentiates GLIs with respect to a scalar
variable.
- FCLoopGLILowerDimension, FCLoopGLIRaiseDimension -
shifts dimensions of GLIs to D-2 or D+2.
- FCLoopAddScalingParameter,
FCLoopGLIExpand - series expansion
of expressions with GLIs with respect to a
scalar variable
- FCLoopIBPReducableQ -
checks if the integral contains propagators raised to integer
powers
- FCLoopIntegralToPropagators
- auxiliary function that converts a loop integral into a list of
propagators
- FCLoopIsolate - wraps loop
integrals into specified heads
- FCLoopMixedIntegralQ -
checks if the integral depends on both 4-vectors and 3-vectors
- FCLoopMixedToCartesianAndTemporal
- eliminates the dependence on 4-vectors by trading them for temporal
components and 3-vectors
- FCLoopNonIntegerPropagatorPowersFreeQ
- checks if the integral has propagators raised to noninteger
powers
- FCLoopPakScalelessQ, FCLoopScalelessQ - detects scaleless
loop integrals
- FCLoopPropagatorPowersCombine
- combines same propagators into one raised to the corresponding integer
power
- FCLoopPropagatorPowersExpand
- rewrites propagators raised to integer powers as products of
propagators
- FCLoopPropagatorsToTopology
- auxiliary function that generates a list of propagators to describe a
topology
- FCLoopRemovePropagator
- removes specific propagators from given
FCTopologys or
GLIs
- FCLoopReplaceQuadraticEikonalPropagators
- tries to eliminate quadratic-eikonal propagators by completing the
square
- FCLoopSamePropagatorHeadsQ
- checks if the integral contains different types of propagators
- FCLoopRemoveNegativePropagatorPowers
- rewrites propagators rasied to negative integer powers as
numerators
- FCLoopSelectTopology -
selects topologies belonging for the given
GLIs
- FCLoopSwitchEtaSign -
changes the sign of i \eta in all
propagators to 1 or -1
- FCLoopSingularityStructure
- useful information on possible UV and IR singularities of the
integral
- FCLoopSolutionList -
auxiliary function that processes the output of FCLoopCanonicalize
- FCLoopSplit - splits the
expressions into pieces that contain different types of loop
integrals
- FCLoopTopologyNameToSymbol
- converts string topology ids to expressions
- FCLoopTensorReduce - tensor
reduction for expressions generated by FCLoopFindTopologies
- FCLoopValidTopologyQ -
validates an FCTopology object
- FCMultiLoopTID - tensor
reduction of multi-loop integrals (only for non-zero Gram
determinants)
- FeynAmpDenominatorCombine -
combines products of propagators
- FeynAmpDenominatorExplicit
- rewrites FeynAmpDenominator
in terms of scalar products and masses
- FeynAmpDenominatorSimplify,
FDS - simplifies loop integrals by doing
shifts and detects integrals that vanish by symmetry
- FeynAmpDenominatorSplit -
splits all FeynAmpDenominators
into products of single propagators
- FromGFAD - tries to convert generic
propagators (GenericPropagatorDenominator)
into the standard ones (StandardPropagatorDenominator,
CartesianPropagatorDenominator)
- GammaExpand - rewrites \Gamma(n+m) where n is an integer
- GenPaVe, PaVe - denotes invariant Passarino-Veltman
integrals
- GLI - represents generic loop multiloop
integrals
- GLIMultiply - local products of GLI objects belonging to the same topology
- Hill - gives the Hill identity
- HypergeometricAC -
analytically continues {}_2 F_1
functions
- HypergeometricIR -
substitutes a particular integral represenetation for all
Hypergeometric2F1[a,b,c,d]
- HypergeometricSE - expresses
hypergeometric functions by their series expansion
- HypExplicit - expresses
hypergeometric functions by their definition in terms of a sum
- HypInt - substitutes {}_2 F_1 functions by their integral
definition
- IntegrateByParts, PartialIntegrate - integration by
parts for particular Feynman parameter integrals
- NPointTo4Point - rewrites
IR-finite 1-loop pentagons in terms of
box integrals
- OneLoopSimplify - simplifies
1-loop Feynman diagram amplitudes
- ToHypergeometric - introduces
{}_2 F_1
- PaVeToABCD - converts PaVe functions to direct (A0, B0 etc.)
functions
- PaVeOrder - orders the arguments of
Passarino-Veltman functions in a particular way
- PaVeLimitTo4 - simplifies
UV-finite D-dimensional expressions
written in terms ofPaVe functions
- PaVeReduce - reduces
Passarino-Veltman integrals down to A_0, B_0,
C_0 and D_0
- PaVeUVPart - returns the
UV-divergent pieces of arbitrary Passarino-Veltman functions
- SimplifyDeltaFunction -
applies some simplifications to DeltaFunction
- Sn - denotes \pi^{(n/2)}/(2 \pi)^n
- TarcerToFC - converts TARCER
integral into FeynAmpDenominator notation
- TFIOrder - orders the arguments of
some
TFI functions in a standard way
- TID - does a 1-loop tensor integral
decomposition
- TIDL - library of tensor integral
decomposition formulas
- ToDistribution - introduces DeltaFunction, DeltaFunctionPrime and PlusDistribution
- ToFI, ToTFI -
converts 1- and 2-loop scalar self-energy integrals to the Tarcer
notation
- ToGFAD - converts FADs, SFADs and CFADs to GFADs
- ToPaVe - converts scalar 1-loop
integrals to Passarino-Veltman scalar functions
- ToPaVe2 - rewrites Passarino-Veltman
functions A0, A00, B0, B1, B00, B11, C0 and D0 as PaVe objects
- ToSFAD - converts FADs to SFADs
- TrickIntegrate - integration of
some special distributions
Export and import
Feynman rules and amplitudes
- BackgroundGluonVertex -
3-gluon vertex in the background field
gauge
- ComplexConjugate - complex
conjugates Feynman amplitudes
- CovariantD - generic covariant
derivative
- CovariantFieldDerivative, CDr - covariant field derivative
- DoPolarizationSums, PolarizationSum - sums over
polarizations of external vector bosons
- ExpandPartialD - expands dot
products of QuantumFields using the
Leibniz rule
- ExplicitPartialD - inserts
the definition for LeftRightPartialD and LeftRightPartialD2
- FAPatch - patches FeynArts to be
compatible with FeynCalc
- FCAttachTypesettingRule, FCRemoveTypesettingRules -
attaches custom typesetting rules
- FCFAConvert - converts a FeynArts
amplitude to FeynCalc
- FCPrepareFAAmp - auxiliary
function for a partial conversion of a FeynArts amplitude to
FeynCalc
- FCTP, FCTripleProduct - triple product in 3
dimensions
- FermionSpinSum - constructs
Dirac traces out of squared ampliudes with external Dirac fermions
- FeynRule - determines Feynman rules
from Lagrangians
- FieldDerivative, FDr - field derivative
- FieldStrength - field strength
tensor F^{\mu \nu}
- FunctionalD - functional
derivative
- GhostPropagator, GHP - ghost propagator
- GluonGhostVertex, GGV - gluon ghost vertex
- GluonPropagator, GP - gluon propagator
- GluonSelfEnergy - 1-loop gluon
self-energy
- GluonVertex, GV - 3- and 4-gluon vertices
- QuarkGluonVertex, QGV - quark gluon vertex
- QuarkPropagator, QP - quark propagator
- ScalarGluonVertex -
scalar-scalar-gluon vertex
- ShiftPartialD - shifts partial
derivatives acting on QuantumFields
using IBPs
- SquareAmplitude - writes |\mathcal{M}|^2 as a list of amplitude
products
- SMP - symbols for various SM
paremeters
- SMVertex - some SM vertices
- ToStandardMatrixElement -
wraps Dirac structures, color structures and polarization vectors with a
special head
- QCDFeynmanRuleConvention -
signs of Feynman rules in some functions
Tables
Options
- $DisableMemSet, $FAPatch, $FCCheckContext, $FCCloudTraditionalForm, $FCTraditionalFormOutput, $FeynArtsDirectory, $FeynCalcDevelopmentVersion,
$FeynCalcDirectory, $FeynCalcLastCommitDateHash
$FeynCalcStartupMessages,
$LoadAddOns, $Multiplications, $RenameFeynCalcObjects, $ParallelizeFeynCalc - global
switches that can be set before loading FeynCalc
- $Containers, $DistributiveFunctions, $DisableMemSet, $FCAdvice, $FCMemoryAvailable, $FCShowIEta, $FortranContinuationCharacter,
$KeepLogDivergentScalelessIntegrals,
$LeviCivitaSign, $LimitTo4, $LimitTo4IRUnsafe, $VeryVerbose, $FAPatch - global switches that can be
changed during the operation of FeynCalc
- $Abbreviations, $AL, $FCTensorList, $FeynCalcVersion, $MU, $NonComm, $ScalarProducts - global variables
needed for the proper functioning of FeynCalc
- A0ToB0, AuxiliaryMomenta, B0Real, B0Unique, Bracket, BReduce, CartesianIndexNames, ClearHeads, Collecting, CombineGraphs, CounterT, CouplingConstant, CustomIndexNames, D0Convention, DetectLoopTopologies, Dimension, DiracIndexNames, DiracSpinorNormalization, DiracTraceEvaluate, Divideout, DotPower, DotSimplifyRelations, DropScaleless, DropSumOver, DummyIndex, EpsDiscard, EpsExpand, EpsilonOrder, EtaSign, ExceptHeads, ExcludeMasses, Expanding, ExtraFactor, ExtraPropagators, ExtraVariables, FactorFull, Factoring, FactoringDenominator, Factorout, FAModelsDirectory, FCDoControl, FCJoinDOTs, FCVerbose, FeynmanIntegralPrefactor, FinalFunction, FinalSubstitutions, ForceSave, FORMAbbreviations, FORMEpilog, FORMIdStatements, FORMProlog, FortranFormatDoublePrecision,
FunctionLimits, Gauge, IncomingMomenta, IndexPosition, InitialFunction, InitialSubstitutions, InsideDiracTrace, InsidePauliTrace, IntegralTable, IntermediateSubstitutions,
IsolateFast, IsolateNames, IsolatePlus, IsolatePrint, IsolateSplit, IsolateTimes, LarinMVV, LightPak, $FCDefaultLightconeVectorN,
$FCDefaultLightconeVectorNB,
Loop, LoopMomenta, LorentzIndexNames, Mandelstam, MultiLoop, NoSave, NumberOfPolarizations, NotMomentum, OtherLoopMomenta, OutgoingMomenta, PairCollect, PartialDRelations, PatchModelsOnly,PauliIndexNames, PauliReduce, PauliTraceEvaluate, PaVeAutoOrder, PaVeAutoReduce, PaVeIntegralHeads, PaVeOrderList, PostFortranFile, Prefactor, PreferredIntegrals, PreferredTopologies, PreFortranFile, PreservePropagatorStructures,
QuarkMass, ReduceGamma, ReduceToScalars, Rename, SameSideExternalEdges, SchoutenAllowNegativeGain,
SchoutenAllowZeroGain, SelectGraphs, SetDimensions, SmallVariables, SplitSymbolicPowers, SubLoop, SubtopologyMarker, SUNFJacobi, SUNIndexNames, SUNFIndexNames, SUNTraceEvaluate, SUNNToCACF, TraceDimension, TraceOfOne, Transversality, TransversePolarizationVectors,
UndoChiralSplittings, UsePaVeBasis, UseTIDL, UseWriteString, VirtualBoson, West, WriteOut,
WriteOutPaVe, WriteStringOutput, ZeroMomentumInsertion - options
of various functions and symbols
Misc
- CalculateCounterTerm, GO, Integratedx,
$MIntegrate, $OPEWard, OPE, OPE1Loop, OPE2TID, OPEDelta, OPEi,
OPEInt, OPEIntegrate, OPEIntegrate2, OPEIntegrateDelta, OPEj, OPEk, OPEl, OPEm, OPEn, OPEo, OPESum, OPESumExplicit, OPESumSimplify, QO, SO, SOD, SymbolicSum2, SymbolicSum3, Twist2AlienOperator, Twist2CounterOperator, Twist2GluonOperator, Twist2QuarkOperator, Twist3QuarkOperator, Twist4GluonOperator - various
(often unfinished and undocumented) functions for QCD OPE
calculations
Deprecated or legacy
functions