The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory

TL;DR

This paper explores the bosonization process in three-dimensional quantum field theory by linking the massive Thirring model with Maxwell-Chern-Simons theory, revealing identities and fractional statistics.

Contribution

It establishes a connection between the massive Thirring model and Maxwell-Chern-Simons theory, providing a bosonization identity and a non-local operator with fractional statistics in 3D.

Findings

Partition functions are identical at lowest order in inverse fermion mass.

Derived a bosonization identity for the fermion current at long length scales.

Presented a non-local operator exhibiting fractional statistics.

Abstract

We discuss bosonization in three dimensions by establishing a connection between the massive Thirring model and the Maxwell-Chern-Simons theory. We show, to lowest order in inverse fermion mass, the identity between the corresponding partition functions; from this, a bosonization identity for the fermion current, valid for length scales long compared with the Compton wavelength of the fermion, is inferred. We present a non-local operator in the Thirring model which exhibits fractional statistics.