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A group SO(3, 2) of point transformations on the space Ω of all (plane) Kepler orbits is introduced. This group has a subgroup of dimension seven induced from point transformations in the configuration plane X = R2 − {0}. In particular X appears as an homogeneous space of SO(2,1), and the (one-parameter family of) invariant connections in this homogeneous space have the configuration space...
We study the Newton–Hooke groups in (2+1)-dimensions. A complete classification of both classical and quantum elementary systems is achieved by explicit computation of coadjoint orbits and unitary irreducible representations of the extended (by central extensions) Newton–Hooke groups. In addition, we show the quantization à la Moyal of a classical system using the Stratonovich–Weyl correspondence...
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