Exotic galilean symmetry, non-commutativity & the Hall effect

TL;DR

This paper explores the connections between exotic Galilean symmetry, non-commutative geometry, and the Hall effect, showing how these concepts interrelate in quantum and field theoretical contexts.

Contribution

It demonstrates how the exotic Galilean symmetry underpins models of the Fractional Quantum Hall Effect and relates to Chern-Simons field theories with non-commutative structures.

Findings

Ground states of the Fractional Quantum Hall Effect derived from exotic particle models

Equations similar to those in quantum Hall systems appear in semiclassical electron models

Exotic Galilean symmetry is shared by certain Chern-Simons field theories

Abstract

The ``exotic'' particle model associated with the two-parameter central extension of the planar Galilei group can be used to derive the ground states of the Fractional Quantum Hall Effect. Similar equations arise for a semiclassical Bloch electron. Exotic Galilean symmetry is also be shared by Chern-Simons field theory of the Moyal type.