The Casimir energy in terms of boundary quantum field theory: the QED case

TL;DR

This paper presents a novel path integral approach to compute the Casimir energy in QED with boundary conditions, demonstrating gauge invariance and extending results to multiple dimensions, including non-vacuum outside conditions.

Contribution

It introduces a boundary quantum field theory framework for Casimir energy calculation in QED, simplifying the process and ensuring gauge invariance, with extensions to various boundary conditions and dimensions.

Findings

Agreement with traditional methods for Casimir energy calculations.

Extension of the approach to non-vacuum exterior conditions.

Gauge invariance naturally incorporated in the boundary field framework.

Abstract

We revisit the path integral computation of the Casimir energy between two infinite parallel plates placed in a QED vacuum. We implement perfectly magnetic conductor boundary conditions (as a prelude to the dual superconductor picture of the QCD vacuum) via constraint fields and show how an effective gauge theory can be constructed for the constraint boundary fields, from which the Casimir energy can be simply computed, in perfect agreement with the usual more involved approaches. Gauge invariance is natural in this framework, as well as the generalization of the result to $d$ dimensions. We also pay attention to the case where the outside of the plates is not the vacuum, but a perfect magnetic (super)conductor, disallowing any dynamics outside the plates. We find perfect agreement between both setups.