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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| Format: | Article |
| Language: | English |
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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 |
| 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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| ISSN: | 1815-0659 |