Noncommutative Phase Spaces by Coadjoint Orbits Method

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.