SISD[p] can be used as input for D-1-dimensional \sigma^{\mu } p_{\mu } with D-dimensional Lorentz vector p and is transformed into PauliSigma[Momentum[p,D],D-1] by FeynCalcInternal.
SISD[p]\sigma \cdot p
SISD[p] // FCI // StandardForm
(*PauliSigma[Momentum[p, D], -1 + D]*)SISD[p, q, r, s](\sigma \cdot p).(\sigma \cdot q).(\sigma \cdot r).(\sigma \cdot s)
SISD[p, q, r, s] // StandardForm
(*SISD[p] . SISD[q] . SISD[r] . SISD[s]*)SISD[q] . (SISD[p] + m) . SISD[q](\sigma \cdot q).(m+\sigma \cdot p).(\sigma \cdot q)