Eur. Phys. J. C (2003) 29: 433-439
https://doi.org/10.1140/epjc/s2003-01205-6

Original Paper

Representations of non-commutative quantum mechanics and symmetries

Theoretical Physics Division, Rudjer Boskovic Institute, P.O. Box 180, 10002, Zagreb, Croatia

^* e-mail: larisa@irb.hr

Abstract

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.