Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concret...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147788 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature / O. Ragnisco, Á. Ballesteros, F.J. Herranz, F. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 42 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548637143269376 |
|---|---|
| author | Ragnisco, O. Ballesteros, A. Herranz, F.J. Musso, F. |
| author_facet | Ragnisco, O. Ballesteros, A. Herranz, F.J. Musso, F. |
| citation_txt | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature / O. Ragnisco, Á. Ballesteros, F.J. Herranz, F. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 42 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.
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| first_indexed | 2025-11-25T20:31:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147788 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:31:25Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ragnisco, O. Ballesteros, A. Herranz, F.J. Musso, F. 2019-02-16T08:10:54Z 2019-02-16T08:10:54Z 2007 Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature / O. Ragnisco, Á. Ballesteros, F.J. Herranz, F. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 42 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37J35; 17B37 https://nasplib.isofts.kiev.ua/handle/123456789/147788 An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). This work was partially supported by the Ministerio de Educaci´on y Ciencia (Spain, Project FIS2004-07913), by the Junta de Castilla y Le´on (Spain, Project VA013C05), and by the INFN–CICyT (Italy–Spain). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature Article published earlier |
| spellingShingle | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature Ragnisco, O. Ballesteros, A. Herranz, F.J. Musso, F. |
| title | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature |
| title_full | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature |
| title_fullStr | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature |
| title_full_unstemmed | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature |
| title_short | Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature |
| title_sort | quantum deformations and superintegrable motions on spaces with variable curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147788 |
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