On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds

TL;DR

This paper explores the feasibility of performing an exact Foldy-Wouthuysen transformation on Dirac spinors in backgrounds with CPT and Lorentz violation, focusing on torsion and related fields, and provides explicit constructions for specific cases.

Contribution

It classifies CPT and Lorentz violating terms that admit an exact Foldy-Wouthuysen transformation and constructs explicit transformations for torsion-related axial vector fields.

Findings

Exact EFWT is possible for certain CPT/Lorentz violating terms.

Explicit EFWT constructed for axial vector torsion with a timelike component.

Perturbative techniques are applicable when EFWT is not feasible.

Abstract

We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix.