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