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

TL;DR

This paper introduces a zeta-function based method for regularizing and renormalizing quantum field fluctuations in curved spacetime, providing finite results and insights into black hole entropy calculations.

Contribution

It presents a novel approach using zeta-function regularization to directly obtain finite quantities and counterterms in curved spacetime quantum field theory.

Findings

Method produces finite, scale-dependent counterterms.

Validated in several examples with known results.

Comments on black hole entropy from induced gravity.

Abstract

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.