Surface Divergences and Boundary Energies in the Casimir Effect

TL;DR

This paper investigates the nature of divergences in Casimir effect calculations, especially focusing on surface divergences and their implications for understanding quantum vacuum energies.

Contribution

It clarifies the role of surface divergences in Casimir energy calculations, resolving controversies about local energy densities and total self-energies.

Findings

Surface divergences are distinct from volume divergences.

Clarification of the interpretation of surface divergences.

Resolution of the contradiction between finite self-energies and divergent local energy densities.

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.