The Casimir effect in chiral media using path integral techniques

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.

25 pages, 6 figures

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• Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
• Parity anomaly with impurities and the Pauli--Villars subtraction
• Casimir effect in magnetic dual chiral density waves
• Topological insulator realization induced by fermionic interaction through BF mediators
• Path-integral approach to Casimir effect with infinitely thin plates