Effective action for $QED_3$ in a region with borders

TL;DR

This paper investigates quantum effects of a Dirac field in 2+1 dimensions confined by boundaries, analyzing the Casimir energy and boundary mode contributions to the effective action in the presence of an external gauge field.

Contribution

It introduces a path-integral approach to evaluate quantum effects in bounded regions and compares large-mass expansion results with bosonized effective theories.

Findings

Derived general results for Casimir energy in bounded regions

Analyzed boundary mode contributions to the effective action

Validated large-mass expansion against bosonized theory

Abstract

We study quantum effects due to a Dirac field in 2+1 dimensions, confined to a spatial region with a non-trivial boundary, and minimally coupled to an Abelian gauge field. To that end, we apply a path-integral representation, which is applied to the evaluation of the Casimir energy and to the study of the contribution of the boundary modes to the effective action when an external gauge field is present. We also implement a large-mass expansion, deriving results which are, in principle, valid for any geometry. We compare them with their counterparts obtained from the large-mass `bosonized' effective theory.