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Noncommutative planar particle dynamics with gauge interactions

Lukierski, J; Stichel, P; Zakrzewski, W.J.

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J Lukierski

P Stichel

W.J. Zakrzewski


We consider two ways of introducing minimal Abelian gauge interactions into the model presented in [Ann. Phys. 260 (1997) 224]. These two approaches are different only if the second central charge of the planar Galilei group is nonzero. One way leads to the standard gauge transformations and the other one to a generalised gauge theory with gauge transformations accompanied by time-dependent area-preserving coordinate transformations. Both approaches, however, are related to each other by a classical Seiberg–Witten map supplemented by a noncanonical transformation of the phase space variables for planar particles. We also formulate the two-body problem in the model with our generalised gauge symmetry and consider the case with both CS and background electromagnetic fields, as it is used in the description of fractional quantum Hall effect.


Lukierski, J., Stichel, P., & Zakrzewski, W. (2003). Noncommutative planar particle dynamics with gauge interactions. Annals of Physics, 306(1), 78-95.

Journal Article Type Article
Publication Date 2003-07
Deposit Date Apr 27, 2007
Publicly Available Date Apr 28, 2009
Journal Annals of Physics
Print ISSN 0003-4916
Electronic ISSN 1096-035X
Publisher Elsevier Masson
Peer Reviewed Peer Reviewed
Volume 306
Issue 1
Pages 78-95


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