The Casimir effect in chiral media using path integral techniques

TL;DR

This paper develops a path integral approach to compute Casimir energies in chiral media, revealing conditions under which repulsive forces can occur, and generalizing boundary conditions in quantum electrodynamics.

Contribution

It introduces a gauge-invariant method using auxiliary fields to analyze Casimir effects in chiral media, extending previous techniques to more complex configurations.

Findings

Method successfully calculates Casimir energies in chiral media.

Results agree with existing literature where comparisons are possible.

Identifies scenarios with repulsive Casimir forces.

Abstract

We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background $\theta$ field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of configurations, and where comparison is possible our results are in perfect agreement with existing literature. Among these are multiple situations where a repulsive Casimir force is possible.