Causal particle detectors and topology

TL;DR

This paper studies how particle detectors respond in topologically non-trivial spacetimes, extending regularization methods to various fields and geometries, and analyzing detector responses in quotient spaces and their embeddings.

Contribution

It extends a regularization technique for the Wightman function to new fields and geometries, and analyzes detector responses in complex topologies and their embeddings.

Findings

Detector responses depend on spacetime topology and motion.

Response is time-dependent for certain motions in quotient spaces.

Embedding Minkowski spaces support the GEMS approach for detector responses.

Abstract

We investigate particle detector responses in some topologically non-trivial spacetimes. We extend a recently proposed regularization of the massless scalar field Wightman function in 4-dimensional Minkowski space to arbitrary dimension, to the massive scalar field, to quotients of Minkowski space under discrete isometry groups and to the massless Dirac field. We investigate in detail the transition rate of inertial and uniformly accelerated detectors on the quotient spaces under groups generated by $(t,x,y,z)\mapsto(t,x,y,z+2a)$, $(t,x,y,z)\mapsto(t,-x,y,z)$, $(t,x,y,z)\mapsto(t,-x,-y,z)$, $(t,x,y,z)\mapsto(t,-x,-y,z+a)$ and some higher dimensional generalizations. For motions in at constant $y$ and $z$ on the latter three spaces the response is time dependent. We also discuss the response of static detectors on the RP^3 geon and inertial detectors on RP^3 de Sitter space via their associated global embedding Minkowski spaces (GEMS). The response on RP^3 de Sitter space, found both directly and in its GEMS, provides support for the validity of applying the GEMS procedure to detector responses and to quotient spaces such as RP^3 de Sitter space and the RP^3 geon where the embedding spaces are Minkowski spaces with suitable identifications.