Euclidean Thermal Green Functions of Photons in Generalized Euclidean Rindler Spaces for any Feynman-like Gauge

The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian case. The coincidence of the found (\be=2\pi)-Green functions and the corresponding Minkowskian vacuum Green functions is discussed in relation to the remaining static gauge ambiguity already found in previous papers. Further generalizations to more complicated manifolds are discussed. Ward identities are verified in the general case.Comment: 12 pages, standard latex, no figures, some signs changed, more comments added, final version to appear on Int. J. Mod. Phys.

Ambiguity in the evaluation of the effective action on the cone

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 non-commutativity of the regularization of ultraviolet and (conical) boundary divergencies.Comment: REVTeX file, 10 pages. Comments on recent papers have been adde

Vacuum Expectation Value of the Spinor Massive field in the Cosmic String Space-Time

We found the contribution to the vacuum expectation value of the energy-momentum tensor of a massive Dirac field due to the conical geometry of the cosmic string space-time. The heat kernel and heat kernel expansion for the squared Dirac operator in this background are also considered and the first three coefficients were found in an explicity form.Comment: 9 pages, 1 figure (2 ref added) (enlarged version

Massive scalar field near a cosmic string

The $\zeta$ 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.Comment: 15 pages, standard LaTeX, no figures. Reference [14] correcte

Thermal partition function of photons and gravitons in a Rindler wedge

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 $\zeta$-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 $s\geq 1$ 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 surface 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.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.

Thermal fluctuations of a quantized massive scalar field in Rindler background

Thermal fluctuations for a massive scalar field in the Rindler wedge are obtained by applying the point-splitting procedure to the zero temperature Feynman propagator in a conical spacetime. Renormalization is implemented by removing the zero temperature contribution. It is shown that for a field of non vanishing mass the thermal fluctuations, when expressed in terms of the local temperature, do not have Minkowski form. As a by product, Minkowski vacuum fluctuations seen by an uniformly accelerated observer are determined and confronted with the literature.Comment: 10 pages; Latex fil

Thermodynamics of scalar fields in Kerr's geometry

The one-loop contributions to the entropy for a massive scalar field in a Kerr black hole are investigated using an approximation of the metric, which, after a conformal transformation, permits to work in a Rindler-like spacetime. Of course, as for the Schwarzschild case, the entropy is divergent in the proximity of the event horizon.Comment: 7 pages, LaTex, (revised version-last section modified

Fluctuations of quantum fields via zeta function regularization

Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that the variance, related to the second functional variation of the effective action, requires a further regularization and that the relative regularized variance turns out to be 2/N, where N is the number of the fields, thus being independent on the dimension D. Some illustrating examples are worked through.Comment: 15 pages, latex, typographical mistakes correcte

Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background

The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Ba\~nados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the $\zeta$-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.Comment: 18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev.

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the paper published in JHE