How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

Details How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

2006-06-15

arxiv.org/abs/gr-qc/0606067v3

Class.Quant.Grav. 23 (2006) 6321-6344

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, 1 figure. v3: Added references and minor clarifications

Scientific paper

10.1088/0264-9381/23/22/015

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.

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