Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background

TL;DR

This paper derives an exact Foldy-Wouthuysen transformation for Dirac particles in combined gravitational wave and magnetic field backgrounds, revealing effects relevant for astrophysics and potential gravitational wave detection methods.

Contribution

It provides an exact transformation and classical limit analysis for Dirac fields in combined gravitational and magnetic backgrounds, a novel approach in this context.

Findings

Gravitational waves influence spinor fields and spinning particles under strong magnetic fields.

The results have potential applications in astrophysics and gravitational wave detection.

The analysis offers a new theoretical framework for understanding Dirac particles in complex backgrounds.

Abstract

We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor field on the combined background of a gravitational wave and constant uniform magnetic field. By taking the classical limit of the spinor field Hamiltonian we arrive at the equations of motion for the non-relativistic spinning particle. Two different kinds of the gravitational fields are considered and in both cases the effect of the gravitational wave on the spinor field and on the corresponding spinning particle may be enforced by the sufficiently strong magnetic field. This result can be relevant for the astrophysical applications and, in principle, useful for creating the gravitational wave detectors based on atomic physics and precise interferometry.