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Separation of Variables in the Elliptic Gaudin Model |
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| Authors: | Evgueni K. Sklyanin Takashi Takebe |
| Affiliation: | St. Petersburg Branch of the Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191011, Russia.?E-mail: sklyanin@pdmi.ras.ru, RU Department of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo, 153-8914, Japan. E-mail: takebe@ms.u-tokyo.ac.jp, JP |
| Abstract: | For the elliptic Gaudin model (a degenerate case of the XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as the poles of a suitably normalized Baker-Akhiezer function. The classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed. The simplest one-degree-of-freedom case is studied in detail. Received: 21 August 1998 / Accepted: 12 January 1999 |
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