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Miscellaneous Applications of Quons
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Miscellaneous Applications of Quons
Інший ID:
2000 Mathematics Subject Classification: 81R50; 81R05; 81R10; 81R15
Посилання:
Miscellaneous Applications of Quons / M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 71 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the 3-rd Microconference “Analytic and Algebraic Methods III”. Some parts of the material reported here were worked out in collaboration with Mohammed Daoud, Olivier Albouy, and Michel Planat. The present paper is a contribution to the 3rd International Microconference “Analytic and Algebraic Methods in Physics” (June 2007, Villa Lanna, Prague); the author is very indebted to Miloslav Znojil for organizing the conference and for useful comments; thanks are due to Uwe G¨unther, Stefan Rauch-Wojciechowski, Artur Sergyeyev, Petr Sulcp, and Pierguilio Tempesta for interesting discussions. This work was also presented at the workshop “Finite Projective Geometries in Quantum Theory” (August 2007, Astronomical Institute, Tatransk´a Lomnica); the author acknowledges the organizer, Metod Saniga, and the other participants for fruitful interactions.
Дата:
2007
Переглядів:
538
Завантажень:
233
Анотація:
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).
