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

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 nonrelativistic spinning particle. Two different kinds of 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 a sufficiently strong magnetic field. This result can be relevant for astrophysical applications and, in principle, useful for creating the gravitational wave detectors based on atomic physics and precise interferometry.