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1+1 Gaudin Model
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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1+1 Gaudin Model
Інший ID:
2010 Mathematics Subject Classification: 14H70; 33E05; 37K20; 37K10
DOI:10.3842/SIGMA.2011.067
DOI:10.3842/SIGMA.2011.067
Посилання:
1+1 Gaudin Model / A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 39 назв. — англ.
Підтримка:
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.
Дата:
2011
Переглядів:
727
Завантажень:
187
Анотація:
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.
