2015/09/05 by James Q. Quach, Quach, James Q.
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #gr-qc
paper · pdf · doi:10.48550/arxiv.1509.01671
4 pages
arxiv created 2015/09/05 · openalex publication_date 2015/09/05 · arxiv updated 2015/09/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.