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

On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation
On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation
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.
4337-4362
World Scientific Publishing
Van der Jeugt, J.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
King, R.C.
94b47e4a-2905-4ba3-a844-ca6c46b6d691
Stoilova, N.I.
c5aabcae-ce39-4841-8183-4d9b531e6546
Palev, T.D.
d76c10dd-851a-4422-b649-fd7b98776e68
Doebner, H.-D.
Dobrev, V.
Van der Jeugt, J.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
King, R.C.
94b47e4a-2905-4ba3-a844-ca6c46b6d691
Stoilova, N.I.
c5aabcae-ce39-4841-8183-4d9b531e6546
Palev, T.D.
d76c10dd-851a-4422-b649-fd7b98776e68
Doebner, H.-D.
Dobrev, V.

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 Publishing. pp. 4337-4362 .

Record type: Conference or Workshop Item (Paper)

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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More information

Published date: 2004
Venue - Dates: Lie Theory and its Applications in Physics V, Fifth International Workshop, Varna, Bulgaria, 2003-06-15 - 2003-06-21

Identifiers

Local EPrints ID: 29533
URI: http://eprints.soton.ac.uk/id/eprint/29533
PURE UUID: 0bb85491-27dd-4147-92f6-5bb3761bfaf7

Catalogue record

Date deposited: 19 May 2006
Last modified: 11 Dec 2021 15:14

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Contributors

Author: J. Van der Jeugt
Author: R.C. King
Author: N.I. Stoilova
Author: T.D. Palev
Editor: H.-D. Doebner
Editor: V. Dobrev

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