The Casimir Effect for Thick Pistons

In this work we analyze the Casimir energy and force for a {\it thick} piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.Comment: LaTex, 21 page

The Casimir effect for pistons with transmittal boundary conditions

This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type $I\times N$ where $I$ is a closed interval of the real line and $N$ is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold $N$ is a $d$-dimensional ball.Comment: 20 pages, LaTe

Asymptotic Expansion of the Heat Kernel Trace of Laplacians with Polynomial Potentials

It is well-known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemmanian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat kernel. It is the purpose of this work to show that, in certain circumstances, termwise integration can be used to obtain the asymptotic expansion of the heat kernel trace for Laplace operators endowed with a suitable polynomial potential on unbounded domains. This is achieved by utilizing a resummed form of the asymptotic expansion of the on-diagonal heat kernel.Comment: 24 Pages, Latex. To appear in Letters in Mathematical Physic

On the Hurwitz Zeta Function of Imaginary Second Argument

In this work we exploit Jonqui\`{e}re's formula relating the Hurwitz zeta function to a linear combination of polylogarithmic functions in order to evaluate the real and imaginary part of $\zeta_{H}(s,ia)$ and its first derivative with respect to the first argument $s$. In particular, we obtain expressions for the real and imaginary party of $\zeta_{H}(s,i a)$ and its derivative for $s=m$ with $m\in\mathbb{Z}\backslash\{1\}$ involving simpler transcendental functions.Comment: LaTeX, 15 page

Vacuum instability in Kaluza-Klein manifolds

The purpose of this work in to analyze particle creation in spaces with extra dimensions. We consider, in particular, a massive scalar field propagating in a Kaluza-Klein manifold subject to a constant electric field. We compute the rate of particle creation from vacuum by using techniques rooted in the spectral zeta function formalism. The results we obtain show explicitly how the presence of the extra-dimensions and their specific geometric characteristics, influence the rate at which pairs of particles and anti-particles are generated.Comment: 19 pages, LaTe

Heat Kernel Asymptotic Expansion on Unbounded Domains with Polynomially Confining Potentials

In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean space. To conduct this study, the trace of the heat kernel is expressed in terms of its partially resummed form which is then represented as a Mellin-Barnes integral. A suitable contour deformation then provides, through the use of Cauchy's residue theorem, closed formulas for the coefficients of the asymptotic expansion. The general expression for the asymptotic expansion, valid for any dimension and any polynomially confining potential, is then specialized to two particular cases: the general quartic and sestic oscillator potentials.Comment: The work has been submitted prematurely and it has therefore been withdraw

Functional determinants and Casimir energy in higher dimensional spherically symmetric background potentials

In this paper we analyze the spectral zeta function associated with a Laplace operator acting on scalar functions on an N-dimensional Euclidean space in the presence of a spherically symmetric background potential. The obtained analytic continuation of the spectral zeta function is then used to derive very simple results for the functional determinant of the operator and the Casimir energy of the scalar field.Comment: 17 pages, LaTe

Some new results for the one-loop mass correction to the compactified λϕ4\lambda\phi^{4} theory

In this work we consider the one-loop effective action of a self-interacting $\lambda\phi^{4}$ field propagating in a $D$ dimensional Euclidean space endowed with $d\leq D$ compact dimensions. The main purpose of this paper is to compute the corrections to the mass of the field due to the presence of the compactified dimensions. Although results for the one-loop correction to the mass of a $\lambda\phi^{4}$ field are very well known for compactified toroidal spaces, where the field obeys periodic boundary conditions, similar results do not appear to be readily available for cases in which the scalar field is subject to Dirichlet and Neumann boundary conditions. We apply the results for the one-loop mass correction to the study of the critical temperature in Ginzburg-Landau models.Comment: 22 pages, Late

Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind

The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory.Comment: 23 pages, LaTe

A Model for the Pioneer Anomaly

In a previous work we showed that massive test particles exhibit a non-geodesic acceleration in a modified theory of gravity obtained by a non-commutative deformation of General Relativity (so-called Matrix Gravity). We propose that this non-geodesic acceleration might be the origin of the anomalous acceleration experienced by the Pioneer 10 and Pioneer 11 spacecrafts.Comment: LaTeX, 12 page