Universal Spin Structure in Gauge Gravitation Theory

TL;DR

This paper introduces a universal spin structure framework in gauge gravitation theory, enabling a unified description of Lorentz spin structures across various gravitational fields.

Contribution

It constructs a composite spinor bundle based on the universal covering group, providing a canonical way to handle spin structures in gauge gravitation theory.

Findings

Defines a composite spinor bundle linked to the universal covering group.

Establishes canonical general covariant transformations of the bundle.

Unifies Lorentz spin structures for different gravitational fields.

Abstract

Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.