Vector Casimir effect for a D-dimensional sphere

Abstract

The Casimir energy or stress due to modes in a D-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensions, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularities) occur for integer dimensions $D\le 1$. Particular attention is given the interesting case of D=2.

20 pages, 1 figure, REVTeX

Cited by in corpus (38)

• New Developments in the Casimir Effect
• The Casimir effect: Recent controversies and progress
• Casimir effect for scalar fields under Robin boundary conditions on plates
• Casimir energy in the MIT bag model
• Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Observability of the Bulk Casimir Effect: Can the Dynamical Casimir Effect be Relevant to Sonoluminescence?
• Casimir Energies and Pressures for $\delta$-function Potentials
• Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries
• Radiative Correction to the Casimir Force on a Sphere
• Casimir Energies for Spherically Symmetric Cavities
• Casimir Energy for Spherical boundaries
• Polarization of the Fulling-Rindler vacuum by uniformly accelerated mirror
• Casimir Energy of a Spherical Shell
• QED with a spherical mirror
• Casimir Effect for Spherical Shell in de Sitter Space
• Casimir stress for concentric spheres in de Sitter space
• Spectral Zeta Functions for a Cylinder and a Circle
• Casimir densities for a spherical boundary in de Sitter spacetime
• Casimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids
• Casimir Energy of a Semi-Circular Infinite Cylinder
• Electromagnetic $\delta$-function sphere
• Casimir densities for a spherical shell in the global monopole background
• Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities
• Comment on Casimir energy for spherical boundaries
• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• Surface Divergences and Boundary Energies in the Casimir Effect
• Casimir energy for spherical shell in Schwarzchild black hole background
• Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
• Sphere-plate Casimir interaction in (D+1)-dimensional spacetime
• Finite temperature Casimir effect on spherical shells in (D+1)-dimensional spacetime and its high temperature limit
• Casimir interaction between spheres in $(\mathbf{D}+1)$-dimensional Minkowski spacetime
• Finite temperature Casimir interaction between spheres in $(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions
• Casimir interaction of concentric spheres at finite temperature
• The Casimir effect for a massless spin-3/2 field in Minkowski spacetime
• Electromagnetic Casimir effect on the boundary of a D-dimensional cavity and the high temperature asymptotics
• Calculation of Ground State Energy for Confined Fermion Fields
• Scalar Casimir effect between two concentric D-dimensional spheres