Vacuum energy in conical space with additional boundary conditions

Abstract

The 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 form of the matching conditions depends on the field under consideration. In the case of the electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions (δ-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of the electromagnetic field and the scalar field, per unit length along the symmetry axis, proves to be finite, unlike the case of an infinitely thin cosmic string. In these studies, the spectral zeta functions are widely used. It is shown briefly how to apply this technique for obtaining the asymptotics of the relevant thermodynamical functions with a high-temperature limit.