Exotic galilean symmetry and non-commutative mechanics in mathematical & in condensed matter physics

TL;DR

This paper explores the exotic Galilean symmetry and non-commutative mechanics, linking them to fractional quantum Hall states and anomalous electron behaviors in condensed matter physics.

Contribution

It introduces a model based on two-parameter central extension of the Galilei group, connecting non-commutative mechanics to quantum Hall phenomena and electron dynamics.

Findings

Derivation of fractional quantum Hall ground states

Discussion of relation to other non-commutative models

Presentation of anomalous coupling effects

Abstract

The ``exotic'' particle model with non-commuting position coordinates, 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. The relation to other NC models is discussed. Anomalous coupling is presented. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.