Functional bosonization of a Dirac field in 2+1 dimensions, in the presence of a boundary

TL;DR

This paper develops a functional bosonization method for a massive Dirac field in 2+1 dimensions with boundaries, revealing boundary conditions and formulating the bosonized action for boundary modes.

Contribution

It introduces a novel bosonization approach for Dirac fields with boundaries, detailing the boundary conditions and the bosonized boundary action.

Findings

Bosonized current form in bulk and boundary modes

Gauge field boundary condition is perfect-conductor

Derived bosonized action for boundary modes

Abstract

We apply the functional bosonization procedure to a massive Dirac field defined on a 2+1 dimensional spacetime which has a non-trivial boundary. We find the form of the bosonized current both for the bulk and boundary modes, showing that the gauge field in the bosonized theory contains a perfect-conductor boundary condition on the worldsheet spanned by the boundary. We find the bononized action for the corresponding boundary modes.