Spin frame transformations and Dirac equations

TL;DR

This paper introduces generalized spin frame transformations that extend traditional spin structures to broader contexts, analyzing their impact on connections and Dirac equations without fixing a metric.

Contribution

It defines new spin frame transformations that are more general than standard ones, allowing extension of spin structures to manifolds without a fixed metric.

Findings

New class of spin frame transformations introduced

Analysis of how these transformations affect connections and Dirac equations

Potential applications in geometry and mathematical physics

Abstract

We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general than usual spin transformations and they usually do not preserve the induced metric structures. We study how these new transformations affect connections both on the spin bundle and on the frame bundle and how this reflects on the Dirac equations.