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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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