Non relativistic SUSY in variants of the planar L\'evy-Leblond equation

TL;DR

This paper demonstrates an N=2 supersymmetry extension of the Schrödinger symmetry in the planar Lévy-Leblond equation, with some supersymmetry surviving in gauged and Chern-Simons coupled versions.

Contribution

It introduces a novel N=2 supersymmetric extension of the Schrödinger symmetry specific to the planar Lévy-Leblond equation and explores its persistence under gauging and Chern-Simons coupling.

Findings

N=2 SUSY exists in the solution space of the free planar Lévy-Leblond equation

Part of the N=2 SUSY survives when the equation is gauged

Some SUSY persists when coupled to Chern-Simons theory

Abstract

An N=2 SUSY extension of the Schr\"odinger symmetry is shown to exist in the solution space of the free planar L\'evy-Leblond equation, an N=1 part of which survives for the gauged version of the equation and also when it is coupled to Chern-Simons theory.