Exotic galilean symmetry in the non-commutative plane, and the Hall effect
Résumé
Quantum Mechanics in the non-commutative plane is shown to admit the ``exotic\'\' symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, 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.