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Construction of the elliptic Gaudin system based on Lie algebra |
| CAO Li-ke, LIANG Hong, PENG Dan-tao, YANG Tao, YUE Rui-hong |
| Institute of Modern Physics, Northwest University, Xi′an 710069, China |
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Abstract Gaudin model is a very important integrable model in both quantum field theory and condensed matter physics. The integrability of Gaudin models is related to classical r-matrices of simple Lie algebras and semi-simple Lie algebra. Since most of the constructions of Gaudin models works concerned mainly on rational and trigonometric Gaudin algebras or just in a particular Lie algebra as an alternative to the matrix entry calculations often presented, in this paper we give our calculations in terms of a basis of the typical Lie algebra, An, Bn, Cn, Dn, and we calculate a classical r-matrix for the elliptic Gaudin system with spin.
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Issue Date: 05 June 2007
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