Curved spacetime gamma matrices (${\gamma }_a=e_a{}^I{\Gamma }_I,\{{\gamma }_a,{\gamma }_b\}=2g_{ab}1$)

An orthonormal coframe converts fixed flat gamma matrices to coordinate-index Clifford multiplication. Its metric identity gives the curved anticommutation relation. The spin connection is chosen so that these matrices are covariantly constant under the combined spin and tensor connection, which is the tetrad postulate in Clifford form.