Perturbative bosonization from two-point correlation functions

TL;DR

This paper develops a method to bosonize massive fermions in 2D and 3D without mass expansion, using two-point correlators to derive a nonlocal bosonic representation that is independent of certain couplings.

Contribution

It introduces a perturbative bosonization approach based on two-point correlators, valid in both 2D and 3D, without relying on fermion mass expansions.

Findings

Derived a bosonic generating functional reproducing correlators

Established the topological conservation of the U(1) current in bosonized form

Mapped fermionic Lagrangian to a nonlocal bosonic Lagrangian independent of couplings

Abstract

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive $QED_2$ and $QED_3$ with $ N $ fermion flavors including also a Thirring coupling. We start from two point correlators involving the U(1) fermionic current and the gauge field. From the tensor structure of those correlators we prove that the U(1) current must be identically conserved (topological) in the corresponding bosonized theory both in D=2 and D=3 dimensions. We find an effective generating functional in terms of bosonic fields which reproduces those two point correlators and from that we obtain a map of the Lagrangian density $\bar{\psi}^{r} (i \partial / - m){\psi}^{r}$ into a bosonic one in both dimensions. This map is nonlocal but it is independent of the eletromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant.