Direct Mode Summation Research Articles

The Casimir Energy for Lorentz-Violating Scalar Field in Sphere

Abstract: In the present article, the Casimir energy was computed for the massless and Lorentz-violating scalar field, confined in a sphere with Dirichlet and Neumann boundary conditions. In 3+1 space-time dimensions, four violated directions to break the Lorentz symmetry are likely, according to which we presented the Casimir energy regarding all possible directions for the Lorentz violation and discussed the pure contribution to the Lorentz violation in a language of graphs. In the details of the calculation, a simple method was developed based on the direct mode summation and the sum-over-modes were performed via the contour integration in a complex plane of eigenfrequencies. The obtained result for all cases of Lorentz symmetry breaking was consistent with the expected physical basis. Keywords: Casimir energy, Lorentz-violating sphere scalar field. PACS No: 11.10.z; 11.10.Gh; 11.25.Db; 11.15.Bt

Extra Dimensions Corrections for Fermionic Casimir Effect in Three Dimensional Box

We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra-dimension. We use the MIT bag model boundary condition for the confinement and M4 × S1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension corrections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.

SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

Fermionic Casimir energy in a three-dimensional box

In this paper we calculate the Casimir energy for a massless fermionic field confined inside a three-dimensional rectangular box. We use the MIT bag model boundary condition for the confinement. We use the direct mode summation method along with the Abel-Plana summation formula to compute the Casimir energy, without any use of regularization or analytic continuation techniques. We obtain a negative Casimir energy, as opposed to the previously reported result for the interior of a three-dimensional sphere.

Casimir energy between two concentric half spheres

We consider the Casimir effect for the massless scalar field between two concentric half spheres. The Casimir energy of a massless scalar field subject to the boundary conditions between two concentric half spheres are calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We devoleped a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions without the use of the asymptotic Debye approximation. All contributions in Casimir energy come from the high frequency modes at fixed ℓ between two surface boundary conditions. We have obtained the negative sign of the Casimir energy for a massless scalar field between two concentric half spheres. The massless scalar field is regarded as interesting both by itself and as the key to describing of the electromagnetic case.

Direct mode summation for the casimir energy of a spherical shell and a compact ball

Direct mode summation for the casimir energy of a spherical shell and a compact ball

Casimir energy of a spherical shell

The Casimir energy for a conducting spherical shell of radius $a$ is computed using a direct mode summation approach. An essential ingredient is the implementation of a recently proposed method based on Cauchy's theorem for an evaluation of the eigenfrequencies of the system. It is shown, however, that this earlier calculation uses an improper set of modes to describe the waves exterior to the sphere. Upon making the necessary corrections and taking care to ensure that no mathematically ill-defined expressions occur, the technique is shown to leave numerical results unaltered while avoiding a longstanding criticism raised against earlier calculations of the Casimir energy.

Direct mode summation for the Casimir energy of a solid ball

The Casimir energy of a solid ball placed in an infinite medium is calculated by a direct frequency summation using the contour integration. It is assumed that the permittivity and permeability of the ball and medium satisfy the condition $\epsilon_1 \mu_1=\epsilon_2\mu_2$. Upon deriving the general expression for the Casimir energy, a dilute compact ball is considered $(\epsilon_1 -\epsilon_2)^2/(\epsilon_1+\epsilon_2)^2\ll 1$. In this case the calculations are carried out which are of the first order in $\xi ^2$ and take account of the five terms in the Debye expansion of the Bessel functions involved. The implication of the obtained results to the attempts of explaining the sonoluminescence via the Casimir effect is shortly discussed.

Simple method for calculating the Casimir energy for a sphere

A simple method for calculating the Casimir energy for a sphere is developed which is based on a direct mode summation and counter integration in a complex plane of eigenfrequencies. The method uses only classical equations determining the eigenfrequencies of the quantum field under consideration. Efficiency of this approach is demonstrated by calculation of the Casimir energy for a perfectly conducting spherical shell and for a massless scalar field obeying the Dirichlet and Neumann boundary conditions on sphere. The possibility of rationalizing the removal of divergences in this problem as a renormalization of both the energy and the radius of the sphere is discussed.