A generally-relativistic gauge classification of the Dirac fields

TL;DR

This paper classifies Dirac fields under relativistic gauge transformations, extending Lounesto's work, and explores implications for dynamics and non-relativistic limits.

Contribution

It introduces a new gauge classification of Dirac fields, providing a comprehensive framework that complements and extends previous classifications like Lounesto's.

Findings

Identifies two exclusive classes of fermions under gauge transformations.

Establishes quantities analogous to momentum and Pauli-Lubanski vectors.

Discusses the non-relativistic approximation within this framework.

Abstract

We consider generally-relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector we discuss how our results are similar to those obtained by Wigner; by taking into account the system of Dirac field equations we will investigate the consequences for the dynamics: and in particular we shall address the problem of getting the non-relativistic approximation in a consistent way. We are going to comment on extensions.