zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times

Details zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times

1997-05-28

arxiv.org/abs/gr-qc/9705077v1

Phys.Lett. B425 (1998) 33-40

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, standard LaTeX, no figures

Scientific paper

10.1016/S0370-2693(98)00209-3

A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at most. These finite couterterms are related to the presence of a particular pole of the effective-action $\zeta$ function as well as to the heat kernel coefficients. The method is checked in several examples obtaining known or reasonable results. Finally, comments are given for as it concerns the recent proposal by Frolov et al. to get the finite Bekenstein-Hawking entropy from Sakharov's induced gravity theory.

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