Local Casimir Energy for a Wedge with circular outer boundary

Abstract

The local Casimir energy is investigated for a wedge with and without a circular outer boundary due to the confinement of a massless scalar field with general curvature coupling parameter and satisfying the Dirichlet boundary conditions. Regularization procedure is carried out making use of a variant of the generalized Abel-Plana formula, previously established by one of the authors. The surface divergences in the vacuum expectation values of the energy density near the boundaries are considered. The corresponding results can be applied to the cosmic strings.

11 pages, 4 figures, discussion of surface divergences extended, new 3D plots, references added, accepted for publication in Class. Quantum Grav

References in corpus (4)

• New Developments in the Casimir Effect
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces
• Casimir Effect for a Dielectric Wedge

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• Repulsive Casimir-Polder forces from cosmic strings
• Casimir densities for a spherical shell in the global monopole background
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Electrodynamic Casimir Effect in a Medium-Filled Wedge II
• Electrodynamic Casimir Effect in a Medium-Filled Wedge
• Vacuum energy in conical space with additional boundary conditions
• Casimir effect at nonzero temperature for wedges and cylinders
• Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary
• Scalar Casimir densities for cylindrically symmetric Robin boundaries
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Summation formula over the zeros of the associated Legendre function with a physical application
• Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media
• Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases