The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local ζ-function regularization approach. The correct Planckian leading order temperature dependence T 4 is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded.It is argued that similar terms could appear dealing with any integer spin s ≥ 1 in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different sur- * Electronic address: iellici@science.unitn.it † Electronic address: moretti@science.unitn.it 1 face terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.

The ζ function of a massive scalar field near a cosmic string is computed and then employed to find the vacuum fluctuation of the field. The vacuum expectation value of the energy-momentum tensor is also computed using a point-splitting approach. The obtained results could be useful also for the case of self-interacting scalar fields and for the finite-temperature Rindler space theory.PACS number(s): 04.62.+v, 04.70.Dy

Abstract:A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the ζ-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 ζ 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. 04.62.+v, 04.70.Dy PACS number(s):

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 -function or heat-kernel approaches working directly in the static manifold containing conical singularities. The relation between the optical method and the direct -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. ͓S0556-2821͑97͒01806-7͔PACS number͑s͒: 04.62.ϩv, 04.70.Dy Another important point is that the optical method produces thermodynamic quantities which agree with those obtained form the point-splitting procedure. This happens in the case of a massless scalar field conformally coupled in the Rindler wedge at least, but also, as we shall see, in the case of the photon field.In the first part of this paper we shall review the compu-*Electronic address: moretti@science.unitn.it † Electronic address: iellici@science.unitn.it PHYSICAL REVIEW D

An ambiguity in the computation of the one-loop effective action for fields living on a cone is illustrated. It is shown that the ambiguity arises due to the noncommutativity of the regularization of ultraviolet and ͑conical͒ boundary divergencies. ͓S0556-2821͑99͒02122-0͔