量子メタマテリアルの幾何学的研究

引力波（GWs）是广义相对论的主要预测之一，今年终于由LIGO合作使用光干涉测量技术直接观测到。最近，由于大质量粒子的引力相互作用增加，物质波干涉测量法被认为是一种潜在的更灵敏的探测gw的方法。有鉴于此，在非相对论极限下理解大质量粒子与GWs的量子相互作用是很重要的。Goncalves等人是第一个在非相对论性极限下，在电磁规范场和gw存在的情况下研究狄拉克哈密顿量的人。在他们的工作中，他们得出了一个有趣的结论，即在GW存在的情况下，即使没有磁场，粒子的自旋也可能进动，他们认为这可能是一种新型GW探测器的基础。我们证明了这种效应不是物理上的，因为它是一个量规变项的结果，这是精确的Foldy-Wouthuysen变换的错误应用的产物。事实上，我们利用精确的和标准的Foldy-Wouthuysen变换，推导出了引力波存在下广义狄拉克哈密顿量的正确的非相对论极限。我们证明了这两个变换一致地产生一个哈密顿量，其中所有项都是规范不变的。然而，不幸的是，这也意味着新的自旋进动效应并不存在。

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.