Optical Approach for the Thermal Partition Function of Photons

Abstract

The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method is applied to the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat's surface terms which instead affect the $\zeta$-function or heat-kernel approaches working directly in the static manifold containing conical singularities. The relation between the optical method and the direct $\zeta$-function approach on the Euclidean Rindler manifold is discussed both in the scalar and the photon cases. Problems with the thermodynamic self-consistency of the results obtained from the stress tensor in the case of the Rindler space are pointed out.

33 pages, RevTeX, no figures. Minor errors corrected, a few Comments changed and some references added since first submission. To be published on Phys.Rev.D

References in corpus (15)

• On Geometric Entropy
• Black Hole Entropy and Entropy of Entanglement
• The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
• On the Description of the Riemannian Geometry in the Presence of Conical Defects
• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• Free and self-interacting scalar fields in the presence of conical singularities
• Remarks on geometric entropy
• Thermodynamics of Quantum Fields in Black Hole Backgrounds
• Comments on information loss and remnants
• Horizon divergences of Fields and Strings in Black Hole backgrounds
• Heat kernels and thermodynamics in Rindler space
• ONE-LOOP QUANTUM CORRECTIONS TO THE ENTROPY FOR A 4-DIMENSIONAL ETERNAL BLACK HOLE
• Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times
• Thermal partition function of photons and gravitons in a Rindler wedge

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• Direct $\zeta$-function approach and renormalization of one-loop stress tensors in curved spacetimes
• Massive scalar field near a cosmic string
• Thermodynamics of scalar fields in Kerr's geometry
• Ultrastatic spacetimes
• Optical geometry for gravitational collapse and Hawking radiation
• Generalized Gravitational Entropy of Interacting Scalar Field and Maxwell Field
• Nontrivial self-consistent backreaction of quantum fields in 2D dilaton gravity
• Aspects and applications of quantum field theory on spaces with conical singularities