Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane

TL;DR

This paper explores the relationship between non-relativistic anyons, exotic Galilean symmetry, and noncommutative geometry, showing how certain models relate to relativistic anyons and how electromagnetic coupling influences their properties.

Contribution

It demonstrates that the Lukierski et al. model can be decomposed into multiple exotic particles and connects noncommutative plane coordinates to exotic Galilean symmetry, revealing their relation to relativistic anyons.

Findings

Decomposition of Lukierski et al. model into independent exotic particles.

Sensitivity of the models to electromagnetic coupling.

Identification of the noncommutative plane as related to exotic Galilean symmetry.

Abstract

We show that the Lukierski et al. model, invariant with respect to the two-fold centrally extended Galilei group, can be decomposed into an infinite number of independent copies (differing in their spin) of the ``exotic'' particle of Duval et al. The difference between the two models is found to be sensitive to electromagnetic coupling. The nature of the noncommutative plane coordinates is discussed in the light of the exotic Galilean symmetry. We prove that the first model, interpreted as describing a non-relativistic anyon, is the non-relativistic limit of a particle with torsion related to relativistic anyons.