Vortex Solutions of a Fermion Maxwell-Chern-Simons Theory

TL;DR

This paper explores vortex solutions in a fermion Maxwell-Chern-Simons theory, demonstrating that it shares static vortex solutions with the Jackiw-Pi model but exhibits distinct vortex dynamics.

Contribution

It introduces a new fermion Maxwell-Chern-Simons theory with consistent static equations and compares its vortex solutions and dynamics to existing models.

Findings

Shares static vortex solutions with Jackiw-Pi model

Exhibits different vortex dynamics

Provides a new consistent fermion Maxwell-Chern-Simons framework

Abstract

We explain how static multi-vortex solutions arise in non-linear field theories, by taking the non-linear Schr\"odinger equation coupled to Chern-Simons field (Jackiw-Pi model) and a fermion Chern-Simons theory as simple examples. We then construct a fermion Maxwell-Chern-Simons theory which has consistent static field equations, and show that it has the same vortex solutions as the Jackiw-Pi model, but gives rise to quite different vortex dynamics.