Cd. Fosco et Fa. Schaposnik, BOSONIZATION OF VECTOR AND AXIAL-VECTOR CURRENTS IN 3+1 DIMENSIONS, Physics letters. Section B, 391(1-2), 1997, pp. 136-143
The bosonization of a massless fermionic field coupled to both vector
and axial-vector external sources is developed, following a path-integ
ral approach. The resulting bosonized theory contains two antisymmetri
c tensor fields whose actions consist of non-local Kalb-Ramond-like te
rms plus interactions. Exact bosonization rules that take the axial an
omaly for the axial current into account are derived, and an approxima
ted bosonized action is constructed.