Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology
A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approx...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149044 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology / J.M. Isidro, P. Fernández de Córdoba // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707977691070464 |
|---|---|
| author | Isidro, J.M. Fernández de Córdoba, P. |
| author_facet | Isidro, J.M. Fernández de Córdoba, P. |
| citation_txt | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology / J.M. Isidro, P. Fernández de Córdoba // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by su(n), for n → ∞. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra su(n).
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| first_indexed | 2025-12-07T17:08:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149044 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:08:37Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Isidro, J.M. Fernández de Córdoba, P. 2019-02-19T13:16:26Z 2019-02-19T13:16:26Z 2008 Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology / J.M. Isidro, P. Fernández de Córdoba // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81T30; 17B56 https://nasplib.isofts.kiev.ua/handle/123456789/149044 A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by su(n), for n → ∞. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra su(n). This paper is a contribution to the Special Issue on Deformation Quantization. It is a great pleasure for J.M.I. to thank Max-Planck-Institut f¨ur Gravitationsphysik, AlbertEinstein-Institut, Golm (Germany) for hospitality during the preparation of this work. The authors thank Generalitat Valenciana (Spain) for financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology Article published earlier |
| spellingShingle | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology Isidro, J.M. Fernández de Córdoba, P. |
| title | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology |
| title_full | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology |
| title_fullStr | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology |
| title_full_unstemmed | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology |
| title_short | Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology |
| title_sort | quantum dynamics on the worldvolume from classical su(n) cohomology |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149044 |
| work_keys_str_mv | AT isidrojm quantumdynamicsontheworldvolumefromclassicalsuncohomology AT fernandezdecordobap quantumdynamicsontheworldvolumefromclassicalsuncohomology |