A formalism for the calculus of variations with spinors

TL;DR

This paper introduces a gauge-independent formalism for the calculus of variations involving spinors, applicable to both spacetime and space spinors, with new operators and explicit variation formulas.

Contribution

It develops a novel gauge-independent formalism for spinorial calculus of variations, including a modified variation operator that simplifies gauge term absorption.

Findings

Defined a gauge-independent variation operator.

Derived explicit variation formulas for connection and curvature spinors.

Applicable to both spacetime and space spinor formalisms.

Abstract

We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As 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.