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

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.

9 pages, standard LaTeX, no figures

References in corpus (5)

• Zeta Functions and the Casimir Energy
• Mechanism of Generation of Black Hole Entropy in Sakharov's Induced Gravity
• Direct $\zeta$-function approach and renormalization of one-loop stress tensors in curved spacetimes
• Massive scalar field near a cosmic string
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Cited by in corpus (16)

• Quantum Scalar Fields on Anti-de Sitter Spacetime
• Quantum fluctuations on a thick de Sitter brane
• Fluctuations of quantum fields via zeta function regularization
• One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure
• Can thick braneworlds be self-consistent?
• Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
• On the Dimensional Reduction Procedure
• Local zeta regularization and the Casimir effect
• An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
• Quantum detectors in generic non flat FLRW space-times
• Scalar Casimir densities and forces for parallel plates in cosmic string spacetime
• Quantum scalar field in D-dimensional static black hole space-times
• Localized thermal states and negative energy
• Vacuum fluctuation of conformally coupled scalar field in FLRW space-times
• Local $\zeta$-functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime
• A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincaré, Online First, 2021)