ImplicitDiracIndex is a data type. It mainly applies to
names of quantum fields specifying that the corresponding field carries
an implicit Dirac index.
This information can be supplied e.g. via
DataType[QuarkField, ImplicitDiracIndex] = True, where
QuarkField is a possible name of the relevant field.
The ImplicitDiracIndex property becomes relevant when
simplifying noncommutative products involving QuantumFields
via ExpandPartialD, DotSimplify.
Overview, DataType, ImplicitSUNFIndex, ImplicitPauliIndex
Default (possibly unwanted) behavior
ex = QuantumField[AntiQuarkField] . GA[\[Mu]] . QuantumField[QuarkField]\bar{\psi }.\bar{\gamma }^{\mu }.\psi
ExpandPartialD[ex]\bar{\gamma }^{\mu }.\bar{\psi }.\psi
Now we let FeynCalc know that AntiQuarkField and
QuarkField carry an implicit Dirac index that connects them
to the Dirac matrix.
DataType[QuarkField, ImplicitDiracIndex] = True;
DataType[AntiQuarkField, ImplicitDiracIndex] = True;ExpandPartialD[ex]\bar{\psi }.\bar{\gamma }^{\mu }.\psi