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1+1 Gaudin Model

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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Bibliographic Details
Main Author: Zotov, A.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147387
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Summary: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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