Effective action for $QED_3$ in a region with borders

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.