Schr\"{o}dinger Fields on the Plane with $[U(1)]^N$ Chern-Simons Interactions and Generalized Self-dual Solitons

TL;DR

This paper studies a non-relativistic field theory on the plane with multiple abelian Chern-Simons gauge fields, revealing fractional statistics, self-dual solutions, and classical vortex configurations, with brief insights into relativistic extensions.

Contribution

It introduces a general framework for non-relativistic fields coupled to multiple Chern-Simons fields, identifying self-dual systems and analyzing classical vortex solutions with mutual statistics.

Findings

Elementary excitations exhibit fractional and mutual statistics.

Self-dual systems allow simplified analysis of classical and quantum properties.

Classical vortex solutions are systematically characterized, including effects of background magnetic fields.

Abstract

A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and non-vanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without uniform background magnetic field. Relativistic generalizations are also discussed briefly.