Quantum Mechanics on a Poincaré Hyperboloid

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...

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Veröffentlicht in:arXiv.org 2015-08
Hauptverfasser: Song, HyunCheol, Jo, Sang Gyu
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Brackets
Charged particles
Mathematical analysis
Quantum mechanics
Quantum theory
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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 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.
ISSN:2331-8422