Particle detectors in curved spacetime quantum field theory

摘要

Unruh-DeWitt particle detector models are studied in a variety oftime-dependent and time-independent settings. We work within the framework offirst-order perturbation theory and couple the detector to a massless scalarfield. The necessity of switching on (off) the detector smoothly is emphasisedthroughout, and the transition rate is found by taking the sharp-switchinglimit of the regulator-free and finite response function. The detector isanalysed on a variety of spacetimes: $d$-dimensional Minkowski, theBa\~nados-Teitelboim-Zanelli (BTZ) black hole, the two-dimensional Minkowskihalf-plane, two-dimensional Minkowski with a receding mirror, and the two- andfour-dimensional Schwarzschild black holes. In $d$-dimensional Minkowskispacetime, the transition rate is found to be finite up to dimension five. Indimension six, the transition rate diverges unless the detector is on atrajectory of constant proper acceleration, and the implications of thisdivergence to the global embedding spacetime (GEMS) methods are studied. Inthree-dimensional curved spacetime, the transition rate for the scalar field inan arbitrary Hadamard state is found to be finite and regulator-free. Then onthe Ba\~nados-Teitelboim-Zanelli (BTZ) black hole spacetime, we analyse thedetector coupled to the field in the Hartle-Hawking vacua, under bothtransparent and reflective boundary conditions at infinity. Results arepresented for the co-rotating detector, which responds thermally, and for theradially-infalling detector. In four-dimensional Schwarzschild spacetime, weproceed numerically, and the Hartle-Hawking, Boulware and Unruh vacua rates arecompared. Results are presented for the case of the static detectors, whichrespond thermally, and also for the case of co-rotating detectors.