Exotic galilean symmetry and the Hall effect

TL;DR

This paper explores how an exotic Galilean symmetry model explains the fractional quantum Hall effect, revealing a singular system at critical magnetic field strength that reduces to Chern-Simons mechanics and exhibits Hall law motion.

Contribution

It introduces a novel approach linking exotic Galilean symmetry to the fractional quantum Hall effect, deriving the Hall law from a reduced Chern-Simons system.

Findings

System becomes singular at critical magnetic field strength.

Reduction yields Chern-Simons mechanics.

System exhibits Hall law motion.

Abstract

The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived using the ``exotic'' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.