Gauge Interactions and Bosonized Fermion Liquids

TL;DR

This paper explores fermion liquids coupled with gauge fields using bosonization, deriving the fermion propagator in 2D with Coulomb and Chern-Simons interactions, relevant to quantum Hall physics.

Contribution

It provides a bosonization-based derivation of the fermion propagator in 2D gauge-interacting fermion liquids, connecting to quantum Hall theories.

Findings

Derived fermion propagator for Coulomb plus Chern-Simons gauge action

Demonstrated consistency with Kohn's theorem

Linked results to Halperin-Lee-Read theory of $ u=1/2$ Landau level

Abstract

We investigate fermion liquids interacting with longitudinal and transverse abelian gauge fields via bosonization. In two spatial dimensions we obtain the fermion propagator for the specific case of a Coulomb plus Chern-Simons gauge action. We discuss the relevance of this result to the Halperin-Lee-Read theory of the $\nu =1/2$ Landau level and demonstrate how Kohn's theorem is satisfied.