Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 092, 14 pages      arXiv:0709.3698      https://doi.org/10.3842/SIGMA.2007.092
Contribution to the Proceedings of the 3-rd Microconference Analytic and Algebraic Methods III

Miscellaneous Applications of Quons

Maurice R. Kibler
Université de Lyon, Institut de Physique Nucléaire, Université Lyon 1 and CNRS/IN2P3, 43 bd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France

Received July 23, 2007, in final form September 21, 2007; Published online September 24, 2007

Abstract
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We motivate why such algebras are interesting for fractional supersymmetric quantum mechanics, angular momentum theory and quantum information. More precisely, quon algebras are used for (i) a realization of a generalized Weyl-Heisenberg algebra from which it is possible to associate a fractional supersymmetric dynamical system, (ii) a polar decomposition of SU2 and (iii) a construction of mutually unbiased bases in Hilbert spaces of prime dimension. We also briefly discuss (symmetric informationally complete) positive operator valued measures in the spirit of (iii).

Key words: quon algebra; q-deformed oscillator algebra; fractional supersymmetric quantum mechanics; polar decompostion of SU2; mutually unbiased bases; positive operator valued measures.

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