Particle detectors in curved space quantum field theory

Abstract

Ambiguities of the particle concept in non-Minkowski spaces are reviewed. To study this and other aspects of quantum field theory in curved spaces, an operationalist approach is adopted through the use of particle detector models. A precise definition of this general concept is given and shown to include many different types of detector models. Five particular models are studied in detail and their responses in Rindler and Schwarzschild spaced are evaluated. In the Rindler case it is explicitly shown that acceleration radiation is anisotropic and time independent. Direct comparison of detectors’ responses is seen to be unsuitable for determining whether two different detectors ‘perceive’ a given situation identically. A method for comparing different detectors is constructed and applied to the models previously introduced. This leads to the notion of equivalence of different detectors, thereby circumventing the problems of direct comparison of their responses. In addition several general results about quantum fields in non-Minkowski spaces are proven. By studying the details of how particle detectors work, the reasons fordifferent detectors being (in)equivalent are revealed. Model detectors of the charged scalar field and spinor fields are then introduced and several problems of “overly simplistic” models are discussed: in particular problems arising from the fact that these fields contain several species of particles. Particle detector equivalence is then applied to these models and used to construct an elementary symmetry between the charged scalar and spinor field many-particle states in the Minkowski Fock space. Finally, a general discussion of several philosophical and practical aspects of using particle detectors to study quantum fields in curved spaces is presented and some points of general confusion are clarified. The particle detector model is operationalist and as such is seen to be most productive when used with close adherence to the Copenhagen interpretation of quantum mechanics.