Casimir effect in the boundary state formalism

TL;DR

This paper presents a boundary state formalism approach to the Casimir effect, providing a large-distance expansion applicable to interacting field theories with a mass gap, avoiding ultraviolet renormalization.

Contribution

It introduces a novel boundary state formalism for the Casimir effect that works for general partially reflecting boundaries and interacting theories with a mass gap.

Findings

Large distance expansion expressed via scattering amplitudes

Formalism applicable to general interacting field theories

No ultraviolet renormalization needed

Abstract

Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.