Perturbative bosonization from two-point correlation functions

Abstract

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive [Formula Presented] and [Formula Presented] with N fermion flavors including also a Thirring coupling. We start from two-point correlators involving the [Formula Presented] fermionic current and the gauge field. From the tensor structure of those correlators we prove that the [Formula Presented] current must be identically conserved (topological) in the corresponding bosonized theory in both [Formula Presented] and [Formula Presented] dimensions. We find an effective generating functional in terms of bosonic fields which reproduces these two-point correlators and from that we obtain a map of the Lagrangian density [Formula Presented][Formula Presented] into a bosonic one in both dimensions. This map is nonlocal but it is independent of the electromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant. © 2003 The American Physical Society.