1+1 Gaudin Model
Mathematical Physics
2011-09-23 v2 High Energy Physics - Theory
Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In case we study the equations in detail and find the corresponding Hamiltonian densities. The -site model describes 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.
Cite
@article{arxiv.1012.1072,
title = {1+1 Gaudin Model},
author = {Andrei V. Zotov},
journal= {arXiv preprint arXiv:1012.1072},
year = {2011}
}