Particle detectors in curved spacetime quantum field theory

Hodgkinson, Lee (2013) Particle detectors in curved spacetime quantum field theory. PhD thesis, University of Nottingham.

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Unruh-DeWitt particle detector models are studied in a variety of time-dependent and time-independent settings. We work within the framework of first-order perturbation theory and couple the detector to a massless scalar field. The necessity of switching on (off) the detector smoothly is emphasised throughout, and the transition rate is found by taking the sharp-switching limit of the regulator-free and finite response function.

The detector is analysed on a variety of spacetimes: d-dimensional Minkowski, the Banados-Teitelboim-Zanelli (BTZ) black hole, the two-dimensional Minkowski half-plane, two-dimensional Minkowski with a receding mirror, and the two- and four-dimensional Schwarzschild black holes.

In d-dimensional Minkowski spacetime, the transition rate is found to be finite up to dimension five. In dimension six, the transition rate diverges unless the detector is on a trajectory of constant proper acceleration, and the implications of this divergence to the global embedding spacetime (GEMS) methods are studied.

In three-dimensional curved spacetime, the transition rate for the scalar field in an arbitrary Hadamard state is found to be finite and regulator-free. Then on the Banados-Teitelboim-Zanelli (BTZ) black hole spacetime, we analyse the detector coupled to the field in the Hartle-Hawking vacua, under both transparent and reflective boundary conditions at infinity. Results are presented for the co-rotating detector, which responds thermally, and for the radially-infalling detector.

Finally, detectors on the Schwarzschild black hole are considered. We begin in two dimensions, in an attempt to gain insight by exploiting the conformal triviality, and where we apply a temporal cut-off to regulate the infrared divergence. In four-dimensional Schwarzschild spacetime, we proceed numerically, and the Hartle-Hawking, Boulware and Unruh vacua rates are compared. Results are presented for the case of the static detectors, which respond thermally, and also for the case of co-rotating detectors.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Louko, J.M.T.
Krasnov, K.
Keywords: Particle detectors, Unruh-DeWitt, black hole, Schwarzschild, BTZ, KMS, thermality, geodesic, transition rate, response function, curved space.
Subjects: Q Science > QA Mathematics > QA611 Topology
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 13636
Depositing User: EP, Services
Date Deposited: 12 Feb 2014 09:52
Last Modified: 13 Sep 2016 12:09

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