SPE[a, b] denotes a D-4-dimensional scalar product. SPE[a, b] is transformed into Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]] by FeynCalcInternal.
SPE[p] is the same as SPE[p,p] (=p^2).
Overview, PD, Calc, ExpandScalarProduct, ScalarProduct, SPD.
SPE[p, q] + SPE[q]\hat{p}\cdot \hat{q}+\hat{q}^2
SPE[p - q, q + 2 p](\hat{p}-\hat{q})\cdot (2 \hat{p}+\hat{q})
Calc[ SPE[p - q, q + 2 p] ]-\hat{p}\cdot \hat{q}+2 \hat{p}^2-\hat{q}^2
ExpandScalarProduct[SPE[p - q]]-2 \left(\hat{p}\cdot \hat{q}\right)+\hat{p}^2+\hat{q}^2
SPE[a, b] // StandardForm
(*SPE[a, b]*)SPE[a, b] // FCI // StandardForm
(*Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]]*)SPE[a, b] // FCI // FCE // StandardForm
(*SPE[a, b]*)FCE[ChangeDimension[SP[p, q], D - 4]] // StandardForm
(*SPE[p, q]*)