Anyon Mean Field as an Exact Limit of a Gauge Theory

TL;DR

This paper analyzes an Abelian gauge theory in 2+1 dimensions with nonrelativistic Fermions, revealing that in a certain limit, Fermions behave as Anyons within an exact mean field framework.

Contribution

It provides an exact solution for the limit where Fermion charge vanishes, showing Fermions behave as Anyons in a gauge theory with Chern-Simons terms.

Findings

Fermions do not fully decouple from the gauge field in the limit.

Fermions behave as Anyons in the mean field approximation.

An exact solution of the gauge theory limit is obtained.

Abstract

We summarize a study of an Abelian gauge theory in 2+1 dimensions, the gauge field being coupled to nonrelativistic Fermions. The Action for the gauge field is a combination of the Maxwell term and a Chern-Simons (CS) term. We study the limit of vanishing Fermions' charge, keeping fixed the gauge field mass induced by the CS term. By considering a closed surface, in particular a torus to keep translational invariance, we show that the Fermions do not decouple completely from the gauge field, and in fact they behave as Anyons treated in the -translationally invariant formulation of the- Mean Field approximation. We describe the exact solution of this limiting case.