Miscellaneous Applications of Quons
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 a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147191 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Miscellaneous Applications of Quons / M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 71 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862544261092737024 |
|---|---|
| author | Kibler, M.R. |
| author_facet | Kibler, M.R. |
| citation_txt | Miscellaneous Applications of Quons / M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 71 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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).
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| first_indexed | 2025-11-25T01:48:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147191 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T01:48:01Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kibler, M.R. 2019-02-13T18:55:17Z 2019-02-13T18:55:17Z 2007 Miscellaneous Applications of Quons / M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 71 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R50; 81R05; 81R10; 81R15 https://nasplib.isofts.kiev.ua/handle/123456789/147191 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). 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Miscellaneous Applications of Quons Article published earlier |
| spellingShingle | Miscellaneous Applications of Quons Kibler, M.R. |
| title | Miscellaneous Applications of Quons |
| title_full | Miscellaneous Applications of Quons |
| title_fullStr | Miscellaneous Applications of Quons |
| title_full_unstemmed | Miscellaneous Applications of Quons |
| title_short | Miscellaneous Applications of Quons |
| title_sort | miscellaneous applications of quons |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147191 |
| work_keys_str_mv | AT kiblermr miscellaneousapplicationsofquons |