Casimir Energy in Non-Covariant Gauges

TL;DR

This paper investigates the Casimir energy for a conducting spherical shell using axial gauge path-integral methods, demonstrating gauge independence and aligning with previous results, thus clarifying gauge invariance in boundary quantum field theory.

Contribution

It introduces a path-integral approach in axial gauge for Casimir energy, showing gauge independence and matching prior Lorenz gauge results, enhancing understanding of boundary effects in quantum fields.

Findings

Complete agreement with Lorenz gauge results

Decoupling of coupled modes via fourth-order differential equations

Clarification of gauge independence in boundary quantum field theory

Abstract

The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the temporal and longitudinal modes for the Maxwell field. The resulting system can be decoupled by studying a fourth-order differential equation with boundary conditions on longitudinal modes and their second derivatives. Complete agreement is found with a previous path-integral analysis in the Lorenz gauge, and with Boyer's value. This investigation leads to a better understanding of how gauge independence is achieved in quantum field theory on backgrounds with boundary.