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. 
C.D. Fosco and F.A. Schaposnik