CSISE[p] can be used as input for D-4-dimensional \sigma^i p^i with D-4-dimensional Cartesian vector p and is
transformed into PauliSigma[CartesianMomentum[p,D-4],D-4]
by FeynCalcInternal.
CSISE[p]\hat{\sigma }\cdot \hat{p}
CSISE[p] // FCI // StandardForm
(*PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]*)CSISE[p, q, r, s]\left(\hat{\sigma }\cdot \hat{p}\right).\left(\hat{\sigma }\cdot \hat{q}\right).\left(\hat{\sigma }\cdot \hat{r}\right).\left(\hat{\sigma }\cdot \hat{s}\right)
CSISE[p, q, r, s] // StandardForm
(*CSISE[p] . CSISE[q] . CSISE[r] . CSISE[s]*)