Vacuum energy in conical space with additional boundary conditions

TL;DR

This paper calculates the finite vacuum energy (Casimir energy) for electromagnetic and scalar fields in conical space with boundary conditions on a cylindrical surface, using spectral zeta functions to analyze thermodynamic limits.

Contribution

It introduces a method to compute finite vacuum energies in conical spaces with various boundary conditions, extending previous work on cosmic strings.

Findings

Casimir energy is finite with boundary conditions, unlike for an idealized cosmic string.

Spectral zeta functions are effectively used to analyze thermodynamics at high temperatures.

Different boundary conditions (perfectly conducting, isorefractive, semi-transparent) are systematically studied.

Abstract

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 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 ($\delta$-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of electromagnetic field and scalar field, per a 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 in the high temperature limit.