Related papers: Zeta-function approach to Casimir energy with sing…
The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet…
In this paper we calculate the Casimir energy for spherical shell with massless self-interacting scalar filed which satisfying Dirichlet boundary conditions on the shell. Using zeta function regularization and heat kernel coefficients we…
Some questions were recently raised about the equivalence of two methods commonly used to compute the Casimir energy: the mode summation approach and the one-loop effective potential. In this respect, we argue that the scale dependence…
The calculation of the minimum of the effective potential using the zeta function method is extremely advantagous, because the zeta function is regular at $s=0$ and we gain immediately a finite result for the effective potential without the…
We compute the Casimir thermodynamic quantities for a massive real scalar field between two parallel plates with the Dirichlet boundary conditions, using three different general approaches and present explicit solutions for each. The…
The new exact formulas for the attractive Casimir force acting on each of the two identical perfectly conducting plates moving freely inside an infinite perfectly conducting cylinder with the same cross section are derived at zero and…
The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary…
We construct various self-similar configurations using parallel $\delta$-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict…
We use the mode summation method together with zeta-function regularization to compute the Casimir energy of a dilute dielectric cylinder. The method is very transparent, and sheds light on the reason the resulting energy vanishes.
The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness $\delta$, where…
A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert…
We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave…
We consider the finite temperature Casimir free energy acting on a spherical shell in (D+1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar and electromagnetic fields. Dirichlet, Neumann, perfectly conducting and…
The contribution of elliptic fixed points to the scalar Casimir energy on compact quotients of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. The expression involves derivatives of…
The response of vacuum to the presence of external conditions is the subject of this work. We consider a generalization of the Casimir effect in the presence of curved boundaries on which a sharp potential is concentrated. The profile of…
We consider an open string with ends laying on the two different solid beams (rods). This set-up is equivalent to two scalar fields with a set of constraints at their end-points. We calculate the zero-point energy and the Casimir energy in…
The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of…
In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is…
The thermal Casimir effect in ideal metal rectangular boxes is considered using the method of zeta functional regularization. The renormalization procedure is suggested which provides the finite expression for the Casimir free energy in any…
Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic…