The role of singular spinor fields in a torsional gravity, Lorentz-violating, framework

TL;DR

This paper explores how singular spinor fields interact with torsional gravity in Lorentz-violating frameworks, revealing their reduced sensitivity to Lorentz violation and differences in coupling compared to Dirac spinors.

Contribution

It demonstrates that singular spinor fields are less affected by Lorentz violation and establishes a mapping between covariant and Lorentz-violating spinor frameworks.

Findings

Singular spinors are less sensitive to Lorentz violation.

Flagpole spinors do not admit minimal torsion coupling.

Mapping between covariant and Lorentz-violating spinors is constructed.

Abstract

In this work, we consider a generalization of quantum electrodynamics including Lorentz violation and torsional-gravity, in the context of general spinor fields as classified in the Lounesto scheme. Singular spinor fields will be shown to be less sensitive to the Lorentz violation, as far as couplings between the spinor bilinear covariants and torsion are regarded. In addition, we prove that flagpole spinor fields do not admit minimal coupling to the torsion. In general, mass dimension four couplings are deeply affected when singular flagpole spinors are considered, instead of the usual Dirac spinors. We also construct a mapping between spinors in the covariant framework and spinors in Lorentz symmetry breaking scenarios, showing how one may transliterate spinors of different classes between the two cases. Specific examples concerning the mapping of Dirac spinor fields in Lorentz violating scenarios into flagpole and flag-dipole spinors with full Lorentz invariance (including the cases of Weyl and Majorana spinors) are worked out.