Covariant Spin Structure

TL;DR

This paper constructs a composite spinor bundle that encompasses all Dirac spin structures on a manifold, allowing for covariant transformations and linking spin structures with gravitational fields.

Contribution

It introduces a new composite spinor bundle framework that includes all Dirac spin structures and supports general covariant transformations.

Findings

Unified framework for Dirac spin structures and gravitational fields

Covariant transformations preserve all Dirac spin structures within the bundle

Enables consistent treatment of spinors in curved spacetime

Abstract

Every Dirac spin structure on a world manifold is associated with a certain gravitational field, and is not preserved under general covariant transformations. We construct a composite spinor bundle such that any Dirac spin structure is its subbundle, and this bundle admits general covariant transformations.