Exotic Galilean Symmetry and the Hall Effect

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.