Different approaches for bosonization in higher dimensions

We describe two distinct approaches for bosonization in higher dimensions; one is based on a direct comparison of current correlation functions while the other relies on a master Lagrangian formalism. These are used to bosonize the massive Thirring model in three and four dimensions in the weak coupling regime but with an arbitrary fermion mass. In both approaches the explicit bosonized Lagrangian and current are derived in terms of gauge fields. The complete equivalence of the two bosonization methods is established. Exact results for the free massive fermion theory are also obtained. Finally, the two-dimensional theory is revisited and the possibility of extending this analysis for arbitrary dimensions is indicated. (C) 1997 Elsevier Science B.V.