This article is cited in 44 papers

Exotic Galilean Symmetry and Non-Commutative Mechanics

Peter A. Horváthy^a, Luigi Martina^bc, Peter C. Stichel<sup>d

a</sup> Laboratoire de Mathématiques et de Physique Théorique, Universit é de Tours, Parc de Grandmont, F-37200 Tours, France
^b Sezione INFN di Lecce, via Arnesano, CP. 193, I-73100 Lecce, Italy
^c Dipartimento di Fisica – Università del Salento
^d An der Krebskuhle 21 D-33 619 Bielefeld, Germany

Abstract: 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.

MSC: 46L55; 37K65; 37L20; 83C65; 81T70

Received: March 23, 2010; in final form July 19, 2010; Published online July 26, 2010

Language: English

DOI: 10.3842/SIGMA.2010.060

Bibliographic databases:

• 
• 
• 

ArXiv: 1002.4772