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| HAL : hal-00502566, version 2 |
| arXiv : 1007.2755 |
| DOI : 10.1016/j.geomphys.2011.02.020 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Geometry and Physics 61, 1 (2011) 1329-1347 |
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| Versions disponibles : | v1 (16-07-2010) | v2 (31-05-2011) |
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| A new integrable system on the sphere and conformally equivariant quantization |
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| Christian Duval 1Galliano Valent 2 |
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| (24/02/2011) |
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| Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi-Moser system, we disclose a novel integrable system on the sphere $S^n$, namely the ''dual Moser'' system. The latter falls, along with the Jacobi-Moser and Neumann-Uhlenbeck systems, into the category of (locally) Stäckel systems. Moreover, it is proved that quantum integrability of both Neumann-Uhlenbeck and dual Moser systems is insured by means of the conformally equivariant quantization procedure. |
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| 1 : | Centre de Physique Théorique (CPT) |
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CNRS : UMR6207 – CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var |
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| 2 : | Laboratoire de Physique Théorique et Hautes Energies (LPTHE) |
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CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| Domaine | : | Physique/Physique mathématique Mathématiques/Physique mathématique Science non linéaire/Systèmes Solubles et Intégrables |
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| Classical integrability – Projectively equivalent metrics – Stäckel systems – Conformally equivariant quantization – Quantum integrability |
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| hal-00502566, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00502566 | |
| oai:hal.archives-ouvertes.fr:hal-00502566 | |
| Contributeur : Christian Duval | |
| Soumis le : Mardi 31 Mai 2011, 16:34:45 | |
| Dernière modification le : Mardi 31 Mai 2011, 16:52:34 | |
