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Representations of noncommutative quantum mechanics and symmetries

Larisa Jonke·Stjepan Meljanac
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Abstract

We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions. Conditions for physical equivalence of different representations of a given system are analysed. Symmetries and classification of phase spaces are discussed. Specially, the dynamical symmetry of a physical system is investigated. Finally, we apply our analyses to the two-dimesional harmonic oscillator and the Landau problem.

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Larisa Jonke, Stjepan Meljanac. 2003-03-14. Representations of noncommutative quantum mechanics and symmetries. https://doi.org/10.1140/epjc%2Fs2003-01205-6

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