Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations

TL;DR

This paper demonstrates that the coupled Chern-Simons and gauged nonlinear Schrödinger equations exhibit non-relativistic conformal symmetry, derived using a non-relativistic Kaluza-Klein approach, highlighting their symmetry properties.

Contribution

It provides a new derivation of the non-relativistic conformal symmetry for these equations via a non-relativistic Kaluza-Klein framework, offering deeper insight into their symmetry structure.

Findings

Non-relativistic conformal symmetry is established for the equations.

The symmetry is derived using a non-relativistic Kaluza-Klein approach.

The work clarifies the geometric origin of the symmetry.

Abstract

The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework.