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Exotic Galilean Symmetry and Non-Commutative Mechanics
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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Some aspects of the “exotic” particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.
Keywords: noncommutative spaces; Galilean symmetry; dynamical systems; quantum field theory. 
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Peter A. Horváthy; Luigi Martina; Peter C. Stichel. Exotic Galilean Symmetry and Non-Commutative Mechanics. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a59/

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