engleski

Representations of noncommutative quantum mechanics and symmetries

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 and a new mechanism for symmetry breaking, originating from (phase) space structure is proposed. Finally, we apply our analyses to the two-dimesional harmonic oscillator and the Landau problem.

deformed harmonic oscillators; quantum mechanics; noncommutative space

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