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arXiv · 1509.01671

Foldy-Wouthuysen transformation of the generalised Dirac Hamiltonian in a gravitational-wave background

James Q. Quach
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Abstract

Goncalves et al. derived a non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using the exact Foldy-Wouthuysen transformation. This gave rise to the intriguing notion that spin-precession may occur even in the absence of a magnetic field. We argue that this effect is not physical as it is the result of a gauge-variant term that was an artefact of a flawed application of the exact Foldy-Wouthuysen transformation. In this paper we derive the correct non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using both the exact and standard Foldy-Wouthuysen transformation. We show that both transformations consistently produce a Hamiltonian where all terms are gauge-invariant. Unfortunately however, we also show that this means the novel spin-precession effect does not exist.

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James Q. Quach. 2015-09-05. Foldy-Wouthuysen transformation of the generalised Dirac Hamiltonian in a gravitational-wave background. https://arxiv.org/abs/1509.01671

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