MomentumCombine[expr] is the inverse operation to
MomentumExpand and ExpandScalarProduct.
MomentumCombine combines also Pairs.
Overview, ExpandScalarProduct, Momentum, MomentumExpand.
Momentum[p] - 2 Momentum[q] // MomentumCombine // StandardForm
(*Momentum[p - 2 q]*)FV[p, \[Mu]] + 2 FV[q, \[Mu]]
ex = MomentumCombine[%]\overline{p}^{\mu }+2 \overline{q}^{\mu }
\left(\overline{p}+2 \overline{q}\right)^{\mu }
ex // StandardForm
(*Pair[LorentzIndex[\[Mu]], Momentum[p + 2 q]]*)ex // ExpandScalarProduct\overline{p}^{\mu }+2 \overline{q}^{\mu }
3 Pair[LorentzIndex[\[Mu]], Momentum[p]] + 2 Pair[LorentzIndex[\[Mu]], Momentum[q]]
ex = MomentumCombine[%]3 \overline{p}^{\mu }+2 \overline{q}^{\mu }
\left(3 \overline{p}+2 \overline{q}\right)^{\mu }
ex // StandardForm
(*Pair[LorentzIndex[\[Mu]], Momentum[3 p + 2 q]]*)In some cases one might need a better control over the types of expressions getting combined. For example, the following expression will not be combined by default, since the coefficients of scalar products are not numbers
DataType[a1, FCVariable] = True;
DataType[a2, FCVariable] = True;ex = SPD[a1 p, n] + SPD[a2 p, nb]\text{a1} (n\cdot p)+\text{a2} (\text{nb}\cdot p)
MomentumCombine[ex]\text{a1} (n\cdot p)+\text{a2} (\text{nb}\cdot p)
Setting the option NumberQ to False we can
still achieve the desired form
MomentumCombine[ex, NumberQ -> False](\text{a1} n+\text{a2} \;\text{nb})\cdot p
However, in the following case combing p^2 with the other two scalar products is not useful
ex = SPD[p] + SPD[a1 p, n] + SPD[a2 p, nb]\text{a1} (n\cdot p)+\text{a2} (\text{nb}\cdot p)+p^2
MomentumCombine[ex, NumberQ -> False]p\cdot (\text{a1} n+\text{a2} \;\text{nb}+p)
To prevent this from happening there is a somewhat hidden option
"Quadratic" that can be set to False
MomentumCombine[ex, NumberQ -> False, "Quadratic" -> False](\text{a1} n+\text{a2} \;\text{nb})\cdot p+p^2
ex = SPD[p] + SPD[a1 p, n] + SPD[a2 p, nb] + SPD[p, l] + SPD[p, k]\text{a1} (n\cdot p)+\text{a2} (\text{nb}\cdot p)+k\cdot p+l\cdot p+p^2
In this case we we would like to prevent the scalar products
involving l and k from being combined with the
rest. To that end we need to use the option Except
MomentumCombine[ex, NumberQ -> False, "Quadratic" -> False, Except -> {k, l}](\text{a1} n+\text{a2} \;\text{nb})\cdot p+k\cdot p+l\cdot p+p^2