Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy

TL;DR

This paper develops a BRST-invariant framework to incorporate dynamical edge modes in Maxwell theory with boundary conditions, enabling the calculation of Casimir energy consistent with physical boundary conditions.

Contribution

It introduces a novel BRST extended formulation for dynamical edge modes in Maxwell theory and applies it to compute Casimir energy with boundary conditions.

Findings

Casimir energy matches that of perfect conductors after BRST implementation

Boundary ghosts ensure BRST invariance of edge mode boundary conditions

Different gauges contribute differently, but results are consistent

Abstract

Recently, dynamical edge modes (DEM) in Maxwell theory have been constructed using a specific local boundary condition on the horizon. We discuss how to enforce this boundary condition on an infinite parallel plate in the QED vacuum by introducing Lagrange multiplier fields into the action. We carefully introduce appropriate boundary ghosts to maintain BRST invariance. Explicit correspondence of this BRST extended theory with the original DEM formulation is discussed, both directly, and through the correspondence between edge modes and Wilson lines attached to the boundary surface. We then use functional methods to calculate the Casimir energy for the first time with DEM boundary conditions imposed on two infinite parallel plates, both in generalized Coulomb and linear covariant gauge. Depending on the gauge, different fields are contributing, but, after correctly implementing the BRST symmetry, we retrieve the exact same Casimir energy as for two perfectly conducting parallel plates.