Casimir Energies in Light of Quantum Field Theory

TL;DR

This paper examines the divergence issues in Casimir energy calculations within quantum field theory, revealing that certain surface-related energies cannot be renormalized independently of the matter-field coupling details.

Contribution

It demonstrates that divergences in Casimir energies near surfaces cannot be absorbed into standard renormalization, challenging previous assumptions about their independence from matter coupling.

Findings

Surface Casimir energies diverge and cannot be renormalized independently.

Energy density away from surfaces remains finite and well-defined.

Force between rigid surfaces is finite and unaffected by coupling details.

Abstract

We study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of the surface and other quantities like the surface tension, which are obtained by deforming the surface, cannot be defined independently of the details of the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and the force between rigid surfaces are finite and independent of these complications.