Vacuum energy in conical space with additional boundary conditions

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.

29 pages, 2 figures, the title was changed for a more adequate one, the abstract was rewritten, a few typos and minor grammar mistakes were corrected

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• Fermionic vacuum polarization by a flat boundary in cosmic string spacetime
• Casimir-Polder interaction between an atom and a conducting wall in cosmic string spacetime
• Finite temperature fermionic condensate in a conical space with a circular boundary and magnetic flux
• Fermionic vacuum polarization around a cosmic string in compactified AdS spacetime
• Scalar Casimir densities and forces for parallel plates in cosmic string spacetime
• Fermionic condensate and the Casimir effect in cosmic string spacetime
• Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime