Quantum Mechanics on a Poincar\'e Hyperboloid
We discuss the process to obtain Poisson brackets among the phase-space variables of a system of a charged particle on a Poincar\'e 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 representat...
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| Sprache: | eng |
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| Zusammenfassung: | We discuss the process to obtain Poisson brackets among the phase-space
variables of a system of a charged particle on a Poincar\'e 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. |
|---|---|
| DOI: | 10.48550/arxiv.1308.5491 |