Two-Component Spinors in Spacetimes with Torsionful Affinities

Abstract

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by the traditional formalisms. Any spin-affine connexion appears to possess a torsional part which is conveniently chosen as a suitable asymmetric contribution. Such a torsional affine contribution thus supplies a gauge-invariant potential that can eventually be taken to carry an observable character, and thereby effectively takes over the role of any trivially realizable symmetric contribution. The overall curvature spinors for any spin-affine connexion accordingly emerge from the irreducible decomposition of a mixed world-spin object which in turn comes out of the action on elementary spinors of a typical torsionful second-order covariant derivative operator. Explicit curvature expansions are likewise exhibited which fill in the gap related to their absence from the literature. It is then pointed out that the utilization of the torsionful spinor framework may afford locally some new physical descriptions.