A formalism for the calculus of variations with spinors

摘要

We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2,C)) 2-spinors as well as to space (i.e., SU(2,C)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors.