Exotic galilean symmetry in the non-commutative plane, and the Hall effect
Abstract
Description
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.
Revised version. The formula for the conserved quantities is corrected; some more references added. 11 pages, LaTex, no figures
Revised version. The formula for the conserved quantities is corrected; some more references added. 11 pages, LaTex, no figures