FVE[p, mu] is the D-4-dimensional vector p with Lorentz index \mu.
Overview, FCE, FCI, FV, FVD, Pair.
FVE[p, \[Mu]]\hat{p}^{\mu }
FVE[p - q, \[Mu]]\left(\hat{p}-\hat{q}\right)^{\mu }
FVE[p, \[Mu]] // StandardForm
(*FVE[p, \[Mu]]*)FCI[FVE[p, \[Mu]]] // StandardForm
(*Pair[LorentzIndex[\[Mu], -4 + D], Momentum[p, -4 + D]]*)There is no special function to expand momenta in FVE.
ex = ExpandScalarProduct[FVE[p - q, \[Mu]]]\hat{p}^{\mu }-\hat{q}^{\mu }
ex // StandardForm
(*Pair[LorentzIndex[\[Mu], -4 + D], Momentum[p, -4 + D]] - Pair[LorentzIndex[\[Mu], -4 + D], Momentum[q, -4 + D]]*)Contract[FVE[p, \[Mu]] FV[q, \[Mu]]]0