Noncommutative Phase Spaces by Coadjoint Orbits Method

[摘要] 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.

[关键词] classical mechanics;noncommutative phase space;coadjoint orbit;symplectic realizations;magnetic and dual magnetic fields