CSPE[p, q] is the D-4-dimensional scalar product of p with q and is transformed into CartesianPair[CartesianMomentum[p, D-4],CartesianMomentum[q, D-4]] by FeynCalcInternal.
CSPE[p] is the same as CSPE[p,p] ( =p^2).
Overview, SPE, ScalarProduct, CartesianScalarProduct.
CSPE[p, q] + CSPE[q]\hat{p}\cdot \hat{q}+\hat{q}^2
CSPE[p - q, q + 2 p](\hat{p}-\hat{q})\cdot (2 \hat{p}+\hat{q})
Calc[ CSPE[p - q, q + 2 p] ]-\hat{p}\cdot \hat{q}+2 \hat{p}^2-\hat{q}^2
ExpandScalarProduct[CSPE[p - q]]-2 \left(\hat{p}\cdot \hat{q}\right)+\hat{p}^2+\hat{q}^2
CSPE[a, b] // StandardForm
(*CSPE[a, b]*)CSPE[a, b] // FCI // StandardForm
(*CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]*)CSPE[a, b] // FCI // FCE // StandardForm
(*CSPE[a, b]*)FCE[ChangeDimension[CSP[p, q], D - 4]] // StandardForm
(*CSPE[p, q]*)