ExplicitLorentzIndex[ind]
is an explicit Lorentz index,
i.e., ind
is an integer.
[LorentzIndex[1], LorentzIndex[\[Mu]]] Pair
\bar{g}^{1\mu }
[LorentzIndex[1], LorentzIndex[\[Mu]]] // StandardForm
Pair
(*Pair[ExplicitLorentzIndex[1], LorentzIndex[\[Mu]]]*)