FreeIndexFreeQ[exp, {head1, head2, ...}] returns True if the expression contains uncontracted indices with heads head1, head2, … and False otherwise.
As always in FeynCalc, Einstein summation convention is implicitly assumed. The function is optimized for large expressions, i.e. it is not so good as a criterion in e.g. Select.
Overview, FCRenameDummyIndices, Contract, DummyIndexFreeQ.
FCI[FV[p, \[Mu]] FV[q, \[Nu]]]
FreeIndexFreeQ[%, {LorentzIndex}]\overline{p}^{\mu } \overline{q}^{\nu }
\text{False}
FCI[FV[p, \[Mu]] FV[q, \[Mu]]]
FreeIndexFreeQ[%, {LorentzIndex}]\overline{p}^{\mu } \overline{q}^{\mu }
\text{True}
FCI[SUNT[a, b]]
FreeIndexFreeQ[%, {SUNIndex}]T^a.T^b
\text{False}
FCI[SUNT[a, a]]
FreeIndexFreeQ[%, {SUNIndex}]T^a.T^a
\text{True}