Quantum Mechanics on a Poincaré Hyperboloid
We discuss the process to obtain Poisson brackets among the phase-space variables of a system of a charged particle on a Poincaré hyperboloid in the presence of a uniform magnetic field. We show that after quantization the Dirac bracket algebra becomes the algebra of ISO(1,2). The representation of this algebra is explicitly analyzed and the Hamiltonian of this system has been derived.
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