On the Chern-Simons Gauge Field

TL;DR

This paper explores the connection between charged particles with magnetic moments in 2+1D electromagnetism and the Chern-Simons gauge field, analyzing both bulk and edge state properties.

Contribution

It establishes a relationship between a particle fluid's electromagnetic and topological currents and examines edge state behavior in bounded regions.

Findings

Topological current relates to electromagnetic current via a simple constitutive relation.

The study clarifies the role of Chern-Simons fields in particle fluids with magnetic moments.

Edge states are characterized when currents are confined to bounded regions.

Abstract

We show the relationship between a fluid of particles having charge and magnetic moment in $2+1$ dimensional electromagnetism and the Chern-Simons statistical field. The matter current which is minimally coupled to the electromagnetic field has two parts: the global electromagnetic current, and the corresponding topological current. The topological current is associated to the induced electromagnetic current, via a simple constitutive relation between charges and magnetic moments. We also study the edge states, when the region that the currents occupy is bounded.