1+1 Gaudin Model
We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densitie...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147387 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 1+1 Gaudin Model / A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862739302617710592 |
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| author | Zotov, A.V. |
| author_facet | Zotov, A.V. |
| citation_txt | 1+1 Gaudin Model / A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau-Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the 2-site case in its own right and describe its relation to the principal chiral model. We emphasize that 1+1 version impose a restriction on a choice of flows on the level of the corresponding 0+1 classical mechanics.
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| first_indexed | 2025-12-07T20:08:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147387 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:08:23Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zotov, A.V. 2019-02-14T16:56:21Z 2019-02-14T16:56:21Z 2011 1+1 Gaudin Model / A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H70; 33E05; 37K20; 37K10 DOI:10.3842/SIGMA.2011.067 https://nasplib.isofts.kiev.ua/handle/123456789/147387 We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau-Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the 2-site case in its own right and describe its relation to the principal chiral model. We emphasize that 1+1 version impose a restriction on a choice of flows on the level of the corresponding 0+1 classical mechanics. Author is grateful to M.A. Olshanetsky for useful discussions and remarks. The work was
 supported by grants RFBR-09-02-00393, RFBR-09-01-92437-KEa, RFBR-09-01-93106-NCNILa, Russian President fund MK-1646.2011.1 and to the Federal Agency for Science and Innovations of Russian Federation under contract 14.740.11.0347. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications 1+1 Gaudin Model Article published earlier |
| spellingShingle | 1+1 Gaudin Model Zotov, A.V. |
| title | 1+1 Gaudin Model |
| title_full | 1+1 Gaudin Model |
| title_fullStr | 1+1 Gaudin Model |
| title_full_unstemmed | 1+1 Gaudin Model |
| title_short | 1+1 Gaudin Model |
| title_sort | 1+1 gaudin model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147387 |
| work_keys_str_mv | AT zotovav 11gaudinmodel |