| 研究実績の概要 |
Gravitational waves (GWs) are one of the major predictions of general relativity that was finally observed directly this year with light interferometry technique by LIGO collaboration. More recently matter-wave interferometry has been proposed as a potentially more sensitive way to detect GWs because of the increased gravitational interaction from the massive particles. In light of this, it is important to understand the quantum interaction of massive particles with GWs in the non-relativistic limit.
Goncalves et al. were the first to investigate the Dirac Hamiltonian in the presence of an electromagnetic (EM) gauge field and GWs, in the non-relativistic limit. In their work, they came to the intriguing conclusion that in the presence of the GW, the particle's spin may precess even in the absence of a magnetic field, which they propose could be the basis for a new type of GW detector. We showed 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. Indeed, we derived 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, this also implies that the novel spin-precession effect does not exist.
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