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

@article{Duval2001ExoticGS,
  title={Exotic Galilean symmetry in the non-commutative plane and the Hall effect},
  author={Christian Duval and P. A.Horv'athy},
  journal={Journal of Physics A},
  year={2001},
  volume={34},
  pages={10097-10107}
}
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. 
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