SISE[p] can be used as input for D-4-dimensional \sigma ^{\mu } p_{\mu } with D-4-dimensional Lorentz vector p and is transformed into
PauliSigma[Momentum[p,D-4], D-4] by
FeynCalcInternal.
SISE[p]\hat{\sigma }\cdot \hat{p}
SISE[p] // FCI // StandardForm
(*PauliSigma[Momentum[p, -4 + D], -4 + D]*)SISE[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)
SISE[p, q, r, s] // StandardForm
(*SISE[p] . SISE[q] . SISE[r] . SISE[s]*)