Exotic galilean symmetry in the non-commutative plane, and the Hall effect

C. Duval; P. A. Horváthy

doi:10.1088/0305-4470/34/47/314

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Exotic galilean symmetry in the non-commutative plane, and the Hall effect

C. Duval·P. A. Horváthy

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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.

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C. Duval, P. A. Horváthy. 2001-07-17. Exotic galilean symmetry in the non-commutative plane, and the Hall effect. https://doi.org/10.1088/0305-4470%2F34%2F47%2F314

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