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Prog. Theor. Phys. Supplement No.118 (1995) pp. 35-60

[ Full Text PDF : FREE ACCESS (2443K) ]

Separation of Variables

— New Trends —

Evgueni K. Sklyanin

Department of Mathematical Sciences, Tokyo University, Tokyo
and
Steklov Mathematical Institute, St. Petersburg

Abstract:

The review is based on the authro's papers since 1985 in which a new approach to the separation of variables (SoV) has being developed. It is argued that SoV, understood generally enough, could be the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard constructuion of the action-angle variables from the poles of the Baker-Akhiezer function can be interpreted as a variant of SoV, and moreover, for many particular models it has a direct quantum counterpart. The list of the models discussed includes XXX and XYZ magnets, Gaudin model, Nonlinear Schrödinger equation, SL(3)-invariant magnetic chain. New results for the 3-particle quantum Calogero-Moser system are reported.


URL : http://ptp.ipap.jp/link?PTPS/118/35/
DOI : 10.1143/PTPS.118.35

[ Full Text PDF : FREE ACCESS (2443K) ] Citation:

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Citing Article(s) :

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  2. Journal of the Physical Society of Japan 66 (1997) pp. 2277-2282 :
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  3. Journal of the Physical Society of Japan 67 (1998) pp. 4045-4050 :
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    Ruguang Zhou and Wen-Xiu Ma
  4. Journal of the Physical Society of Japan 68 (1999) pp. 380-385 :
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    Kazuhiro Hikami and Rei Inoue
  5. Progress of Theoretical Physics Supplement No.135 (1999) pp. 211-233 :
    Integrability of High-Energy QCD
    Gregory P. Korchemsky

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