Covariant differentiation of spinors for a general affine connection

Abstract

We show that the covariant derivative of a spinor for a general affine connection, not restricted to be metric compatible, is given by the Fock-Ivanenko coefficients with the antisymmetric part of the Lorentz connection. The projective invariance of the spinor connection allows to introduce gauge fields interacting with spinors. We also derive the relation between the curvature spinor and the curvature tensor for a general connection.