Anyons and the Landau problem in the noncommutative plane

TL;DR

This paper explores the Landau problem within a noncommutative plane framework, linking it to anyon theory and the planar Galilei group's realizations, offering insights into quantum behavior in noncommutative geometries.

Contribution

It introduces a novel analysis connecting the Landau problem, noncommutative geometry, and anyon theory through group realizations.

Findings

Establishes a relationship between noncommutative Landau problem and anyon models.

Provides a group-theoretical framework for understanding quantum particles in noncommutative spaces.

Suggests new avenues for studying quantum Hall effects in noncommutative geometries.

Abstract

The Landau problem in the noncommutative plane is discussed in the context of realizations of the two-fold centrally extended planar Galilei group and the anyon theory.