CGAD[i] can be used as input for \gamma ^i in D dimensions, where i is a Cartesian index, and is transformed into DiracGamma[CartesianIndex[i,D-1],D] by FeynCalcInternal.
CGAD[i]\gamma ^i
CGAD[i, j] - CGAD[j, i]\gamma ^i.\gamma ^j-\gamma ^j.\gamma ^i
StandardForm[FCI[CGAD[i]]]
(*DiracGamma[CartesianIndex[i, -1 + D], D]*)CGAD[i, j, k, l]\gamma ^i.\gamma ^j.\gamma ^k.\gamma ^l
StandardForm[CGAD[i, j, k, l]]
(*CGAD[i] . CGAD[j] . CGAD[k] . CGAD[l]*)DiracSimplify[DiracTrace[CGAD[i, j, k, l]]]4 \delta ^{il} \delta ^{jk}-4 \delta ^{ik} \delta ^{jl}+4 \delta ^{ij} \delta ^{kl}
CGAD[i] . (CGSD[p] + m) . CGAD[j]\gamma ^i.(m+\gamma \cdot p).\gamma ^j