Exotic Galilean symmetry in the non-commutative plane and the Hall effect

By C. Duval, P. Horváthy. 2001

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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 et al. The reduced system moves according to the Hall law.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6879bb63252532b8850fddd755819074beb5e12e