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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National Academy of Science of Ukraine
2011-07-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.067 |
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doaj-4c8fba0747eb455383cf9d3a7d9af1d62020-11-24T23:08:57ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-07-0170671+1 Gaudin ModelAndrei V. ZotovWe 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.http://dx.doi.org/10.3842/SIGMA.2011.067integrable systemsfield theoryGaudin models |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Andrei V. Zotov |
| spellingShingle |
Andrei V. Zotov 1+1 Gaudin Model Symmetry, Integrability and Geometry: Methods and Applications integrable systems field theory Gaudin models |
| author_facet |
Andrei V. Zotov |
| author_sort |
Andrei V. Zotov |
| title |
1+1 Gaudin Model |
| title_short |
1+1 Gaudin Model |
| title_full |
1+1 Gaudin Model |
| title_fullStr |
1+1 Gaudin Model |
| title_full_unstemmed |
1+1 Gaudin Model |
| title_sort |
1+1 gaudin model |
| publisher |
National Academy of Science of Ukraine |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| issn |
1815-0659 |
| publishDate |
2011-07-01 |
| 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. |
| topic |
integrable systems field theory Gaudin models |
| url |
http://dx.doi.org/10.3842/SIGMA.2011.067 |
| work_keys_str_mv |
AT andreivzotov 11gaudinmodel |
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