Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 116, 12 pages      arXiv:1102.0718      https://doi.org/10.3842/SIGMA.2011.116

Noncommutative Phase Spaces by Coadjoint Orbits Method

Ancille Ngendakumana a, Joachim Nzotungicimpaye b and Leonard Todjihounde a
a) Institut de Mathématiques et des Sciences Physiques, Porto-Novo, Benin
b) Kigali Institute of Education, Kigali, Rwanda

Received May 24, 2011, in final form December 13, 2011; Published online December 18, 2011

Abstract
We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.

Key words: classical mechanics; noncommutative phase space; coadjoint orbit; symplectic realizations; magnetic and dual magnetic fields.

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