CSPD[p, q] is the D-1-dimensional scalar product of p with q and is transformed into CartesianPair[CartesianMomentum[p, D-1],CartesianMomentum[q, D-1]] by FeynCalcInternal.
CSPD[p] is the same as CSPD[p,p] (=p^2).
Overview, SPD, ScalarProduct, CartesianScalarProduct.
CSPD[p, q] + CSPD[q]p\cdot q+q^2
CSPD[p - q, q + 2 p](p-q)\cdot (2 p+q)
Calc[ CSPD[p - q, q + 2 p] ]-p\cdot q+2 p^2-q^2
ExpandScalarProduct[CSPD[p - q]]-2 (p\cdot q)+p^2+q^2
CSPD[a, b] // StandardForm
(*CSPD[a, b]*)CSPD[a, b] // FCI // StandardForm
(*CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]*)CSPD[a, b] // FCI // FCE // StandardForm
(*CSPD[a, b]*)FCE[ChangeDimension[CSP[p, q], D]] // StandardForm
(*CSPD[p, q]*)