Related papers: The generalized Abel-Plana formula with applicatio…
Positive frequency Wightman function and vacuum expectation value of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel plates…
In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic…
This is the first one of a series of papers about zeta regularization of the divergences appearing in the vacuum expectation value (VEV) of several local and global observables in quantum field theory. More precisely we consider a…
We propose a procedure for the renormalization of Casimir energy, that is based on the implicit versions of standard steps of renormalization procedure --- regularization, subtraction and removing the regularization. The proposed procedure…
The neglected Russian mathematician, N.~S.~Koshliakov, derived beautiful generalizations of the classical Abel--Plana summation formula through a setting arising from a boundary value problem in heat conduction. When we let the parameter…
We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard…
The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel-Plana formula is used for renormalization of divergent series in the condensate…
The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series.…
The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
In the $(\epsilon_1-\epsilon_2)^2$--approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a…
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function…
The next to the leading order Casimir effect for a real scalar field, within $\phi^4$ theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Green's function with the Dirichlet boundary…
We investigate the renormalized vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field inside and outside of a conducting cylindrical shell in the cosmic string spacetime. By using the…
We calculate the Casimir energy for scalar fields in interaction with finite-width mirrors, described by nonlocal interaction terms. These terms, which include quantum effects due to the matter fields inside the mirrors, are approximated by…
In this paper we investigate the vacuum polarization effects associated with a massive fermionic field due to the non-trivial topology of the global monopole spacetime and boundary conditions imposed on this field. Specifically we…
This paper continues the investigation of the Casimir effect with the use of the algebraic formulation of quantum field theory in the initial value setting. Basing on earlier papers by one of us (AH) we approximate the Dirichlet and Neumann…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
In the present paper we study equations of state of Casimir vacuum of massive scalar field and massive bispinor field in compact Friedmann Universe. With use of the Abel-Plana formula the renormalization of divergent series for calculation…
We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In…