Considerations on the Unruh Effect: Causality and Regularization

Details Considerations on the Unruh Effect: Causality and Regularization Considerations on the Unruh Effect: Causality and Regularization

2003-06-05

arxiv.org/abs/gr-qc/0306022v2

Class.Quant.Grav. 21 (2004) 4647-4660

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 2 figures, v2: some minor changes

Scientific paper

10.1088/0264-9381/21/19/011

This article is motivated by the observation, that calculations of the Unruh effect based on idealized particle detectors are usually made in a way that involves integrations along the {\em entire} detector trajectory up to the infinitely remote {\em future}. We derive an expression which allows time-dependence of the detector response in the case of a non-stationary trajectory and conforms more explicitely to the principle of causality, namely that the response at a given instant of time depends only on the detectors {\em past} movements. On trying to reproduce the thermal Unruh spectrum we are led to an unphysical result, which we trace down to the use of the standard regularization $t\to t-i\eps$ of the correlation function. By consistently employing a rigid detector of finite extension, we are led to a different regularization which works fine with our causal response function.

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