Bosonization in more than two spacetime dimensions

A low-momentum path-integral bosonization method for more than two spacetime dimensions is extended in two different directions: We first consider the 2 + 1 dimensional case. By keeping the full momentum-dependence of the one-loop vacuum polarization tensor, we can discuss both the massive and massless fermion cases on an equal footing. Results for massless fermions coincide with the ones of a different, (operatorial) approach to the problem of bosonization for a massless fermionic field. Secondly, the bosonization of a massless fermionic field coupled to both vector and axial-vector external sources in 3 + 1 dimensions is developed. The resulting bosonic theory contains two antisymmetric tensor fields with non-local Kalb-Ramond-like terms plus interactions. Exact bosonization rules that take the axial anomaly into account are derived.