Representations of non-commutative quantum mechanics and symmetries
Theoretical Physics Division, Rudjer Boskovic Institute, P.O. Box 180, 10002, Zagreb, Croatia
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We present a unified approach to representations of quantum mechanics on non-commutative spaces with general constant commutators of the phase-space variables. We find two phases and duality relations among them in arbitrary dimensions. Conditions for the physical equivalence of different representations of a given system are analyzed. Symmetries and classification of phase spaces are discussed. Especially, the dynamical symmetry of a physical system is investigated. Finally, we apply our analyses to the two-dimensional harmonic oscillator and the Landau problem.
© Springer-Verlag, 2003