CSID[i] can be used as input for D-1-dimensional \sigma^i with D-1-dimensional Cartesian index i and is transformed into PauliSigma[CartesianIndex[i,D-1],D-1] by FeynCalcInternal.
CSID[i]\sigma ^i
CSID[i, j] - CSID[j, i]\sigma ^i.\sigma ^j-\sigma ^j.\sigma ^i
StandardForm[FCI[CSID[i]]]
(*PauliSigma[CartesianIndex[i, -1 + D], -1 + D]*)CSID[i, j, k, l]\sigma ^i.\sigma ^j.\sigma ^k.\sigma ^l
StandardForm[CSID[i, j, k, l]]
(*CSID[i] . CSID[j] . CSID[k] . CSID[l]*)