Surface Divergences and Boundary Energies in the Casimir Effect

Abstract

Although Casimir, or quantum vacuum, forces between distinct bodies, or self-stresses of individual bodies, have been calculated by a variety of different methods since 1948, they have always been plagued by divergences. Some of these divergences are associated with the volume, and so may be more or less unambiguously removed, while other divergences are associated with the surface. The interpretation of these has been quite controversial. Particularly mysterious is the contradiction between finite total self-energies and surface divergences in the local energy density. In this paper we clarify the role of surface divergences.

arXiv comment8 pages, 1 figure, submitted to proceedings of QFEXT05

References in corpus (13)

• The Casimir effect: Recent controversies and progress
• Casimir effect for scalar fields under Robin boundary conditions on plates
• Casimir effect for a $D$-dimensional sphere
• The Dirichlet Casimir Problem
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
• Casimir Energies and Pressures for $\delta$-function Potentials
• Nonsmooth backgrounds in quantum field theory
• Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces
• Vector Casimir effect for a D-dimensional sphere
• Calculating Casimir Energies in Renormalizable Quantum Field Theory
• The heat kernel expansion for the electromagnetic field in a cavity
• The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

Cited by in corpus (12)

• Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
• Casimir stress in an inhomogeneous medium
• Electromagnetic field fluctuations near a dielectric-vacuum boundary and surface divergences in the ideal conductor limit
• Vacuum energy densities of a field in a cavity with a mobile boundary
• Electromagnetic Casimir energy with extra dimensions
• Vacuum Casimir energy densities and field divergences at boundaries
• Casimir effect for scalar current densities in topologically nontrivial spaces
• A Fluid Analog Model for Boundary Effects in Field Theory
• Resolution of an apparent inconsistency in the electromagnetic Casimir effect
• Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
• Inhomogeneity-related cutoff dependence of the Casimir energy and stress
• The Phononic Casimir Effect: An Analog Model