Construction of the elliptic Gaudin system based on Lie algebra |
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Authors: | Cao Li-ke Liang Hong Peng Dan-tao Yang Tao and Yue Rui-hong |
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Institution: | (1) 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, A
n
, B
n
, C
n
, D
n
, and we calculate a classical r-matrix for the elliptic Gaudin system with spin.
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Keywords: | Gaudin model classical r-matrix Lie algebra elliptic function |
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