Exotic galilean symmetry in the non-commutative plane, and the Hall effect
High Energy Physics - Theory
2008-11-26 v3 Condensed Matter
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0106089,
title = {Exotic galilean symmetry in the non-commutative plane, and the Hall effect},
author = {C. Duval and P. A. Horváthy},
journal= {arXiv preprint arXiv:hep-th/0106089},
year = {2008}
}
Comments
Revised version. The formula for the conserved quantities is corrected; some more references added. 11 pages, LaTex, no figures