Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane

TL;DR

This paper develops a covariant framework for supersymmetric anyons in 2+1 dimensions using Wigner's algebra deformation, leading to non-relativistic equations for particles on a non-commutative plane with exotic supersymmetry.

Contribution

It introduces a novel covariant set of equations for supersymmetric anyons based on Wigner's algebra deformation, connecting relativistic and non-relativistic descriptions.

Findings

Derivation of first-order wave equations for spinning particles on non-commutative planes.

Establishment of Galilean exotic N=1 supersymmetry in the non-relativistic limit.

Linking of relativistic anyon models to non-commutative geometry.

Abstract

A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic ``Jackiw-Nair'' limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N=1 supersymmetry.