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

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 bosonized action for the corresponding boundary modes.