On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation

Van der Jeugt, J., King, R.C., Stoilova, N.I. and Palev, T.D. (2004) On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation. Doebner, H.-D. and Dobrev, V. (eds.) In Lie Theory and its Applications in Physics V: Proceedings of the Fifth International Workshop, Varna, Bulgaria 16-22 June 2003. World Scientific. pp. 4337-4362 .

Abstract

After a general introduction to Wigner Quantum Systems, we define the three-dimensional n-particle Wigner Quantum Oscillator, and its relation to the Lie superalgebra sl(1|3n). In this framework, coordinates, momentum and the angular momentum of the particles are defined and investigated. This investigation is done in state spaces, using representation theory of sl(1|3n). For the case of n=1, the main properties are listed, with an emphasis on the non-commutative coordinates of the particle and its unconventional consequences. For general n, we study energy spectra, angular momentum, and in particular the particle configuration and its interpretation. Throughout, a comparison with the canonical oscillator solution is given.

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