Bosonization of vector and axial-vector currents in 3 + 1 dimensions

The bosonization of a massless fermionic field coupled to both vector and axial-vector external sources is developed, following a path-integral approach. The resulting bosonized theory contains two antisymmetric tensor fields whose actions consist of non-local Kalb-Ramond-like terms plus interactions. Exact bosonization rules that take the axial anomaly for the axial current into account are derived, and an approximated bosonized action is constructed.