Related papers: Mode-by-mode summation for the zero point electrom…
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.
We examine the Casimir effect for a perfectly conducting cylinder of elliptical section, taking as reference the known case of circular section. The zero-point energy of this system is evaluated by the mode summation method, using the…
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of…
A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in…
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…
Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit…
We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding…
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…
A rigorous formulation of the problem of calculating the electromagnetic vacuum energy of an infinite dielectric cylinder is discussed. It is shown that the physically relevant spectrum of electromagnetic excitations includes the surface…
Values for the vacuum energy of scalar fields under Dirichlet and Neuman boundary conditions on an infinite clylindrical surface are found, and they happen to be of opposite signs. In contrast with classical works, a complete zeta function…
The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in $\xi^2$ and numerically to higher orders in $\xi^2$. The first part is carried out using…
We compute the Casimir interaction energy between two perfectly conducting, concentric cylinders, using the mode-by-mode summation technique. Then we compare it with the approximate results obtained using the proximity theorem and a…
We discuss new approaches to compute numerically the Casimir interaction energy for waveguides of arbitrary section, based on the boundary methods traditionally used to compute eigenvalues of the 2D Helmholtz equation. These methods are…
The finite temperature Casimir free energy is calculated for a dielectric ball of radius $a$ embedded in an infinite medium. The condition $\epsilon\mu=1$ is assumed for the inside/outside regions. Both the Green function method and the…
The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the…
In this paper we sum over the spherical modes appearing in the expression for the Casimir energy of a conducting sphere and of a dielectric ball (assuming the same speed of light inside and outside), before doing the frequency integration.…
New exact results are given for the interior Casimir energies of infinitely long waveguides of triangular cross section (equilateral, hemiequilateral, and isosceles right triangles). Results for cylinders of rectangular cross section are…
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…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
The Casimir energy of an infinite compact cylinder placed in a uniform unbounded medium is investigated under the continuity condition for the light velocity when crossing the interface. As a characteristic parameter in the problem the…