On the Casimir effect with mixed dynamical edge mode and perfect electromagnetic conducting boundary conditions

TL;DR

This paper investigates the Casimir effect between plates with mixed boundary conditions, revealing that a dynamical edge mode plate behaves like a perfect magnetic conductor plate in terms of Casimir force.

Contribution

It introduces a novel boundary condition setup with dynamical edge modes and demonstrates their equivalence to PMC boundary conditions in Casimir force calculations.

Findings

Casimir force with DEM boundary conditions matches that with PMC conditions.

Restoring BRST invariance requires new edge fields on the DEM plate.

The effective boundary theory is non-local and derived from the bulk action.

Abstract

We study the Casimir effect for a parallel plate setup with one plate with dynamical edge mode (DEM) boundary conditions, and one plate with perfect electromagnetic conductor (PEMC) boundary conditions. In order to restore BRST invariance, new edge fields are introduced on the DEM plate. We then lift the boundary conditions into the action using Lagrange multiplier fields, and integrate out the bulk fields to obtain a non-local effective boundary theory from which we compute the Casimir energy. The resulting Casimir force is identical to a PMC-PEMC setup, implying that, from the point of view of the Casimir effect, a DEM plate is equivalent to a PMC plate. We also include a detailed derivation of the general functional method used to compute the Casimir energy from the partition function.