Inquiring the Unruh–DeWitt detector about the global property of spacetime

Abstract

Abstract We investigate the effect of spatial compactification on the transition rate of an inertial or accelerated Unruh–Dewitt detector coupled to an untwisted or twisted massless quantum scalar field. Four typical cases of the detector’s motion in the compactified Minkowski spacetime are considered respectively. Our results indicate that the detector’s transition rates are crucially dependent on the spatial compactification length, the magnitude and direction of detector’s velocity, the detector’s acceleration, and the field structure. As these factors change, the detector’s spontaneous emission and absorption processes can be enhanced or weakened at different degrees. In particular, when the compact length is small, the behavior of transition rate in the case of the twisted field is quite distinct from that of the untwisted field. Notably, when the detector moves at a constant velocity with nonzero components along the compact and non-compact directions, our study finds that the spontaneous emission rate depends on the component of velocity along the non-compact direction besides that along the compact direction. This is in sharp contrast with the case of the free Minkowski spacetime. Moreover, for the uniformly accelerated detector along the non-compact direction, the spatial compactification clearly modifies both the spontaneous emission and absorption rates, as the modifying factors depend on the compact length and the detector’s acceleration. Our work indirectly but comprehensively examines the nonequivalence of inertial frames in the compactified Minkowski spacetime, and meanwhile provides a theoretical way to identify the orientation and the size of the compact spatial dimension.