The Casimir energy with perfect electromagnetic boundary conditions and duality: a field-theoretic approach

TL;DR

This paper investigates the Casimir effect between parallel plates with perfect electromagnetic boundary conditions using a field-theoretic approach, highlighting boundary contributions and electromagnetic duality invariance.

Contribution

It introduces a novel field-theoretic method to analyze the Casimir effect with electromagnetic boundary conditions and explores the role of duality symmetry in this context.

Findings

Recovered the Casimir energy via path integral and energy-momentum tensor methods.

Identified boundary contributions to the energy-momentum tensor.

Analyzed electromagnetic duality invariance and its relation to boundary conditions.

Abstract

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral, and once as the vacuum expectation value of the 00-component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified, and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality-invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation.