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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 067, 26 pages      arXiv:1012.1072      http://dx.doi.org/10.3842/SIGMA.2011.067

1+1 Gaudin Model

Andrei V. Zotov
Institute of Theoretical and Experimental Physics, Moscow, Russia

Received January 29, 2011, in final form July 03, 2011; Published online July 13, 2011

Abstract
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.

Key words: integrable systems; field theory; Gaudin models.

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