dorsal/arxiv
View SchemaSeparation of Variables. New Trends.
| Authors | E. K. Sklyanin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9504001 |
| URL | https://arxiv.org/abs/solv-int/9504001 |
| DOI | 10.1143/PTPS.118.35 |
| Journal | Prog.Theor.Phys.Suppl.118:35-60,1995 |
Abstract
The review is based on the author'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 construction 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 Schr\"odinger equation, $SL(3)$-invariant magnetic chain. New results for the 3-particle quantum Calogero-Moser system are reported.
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"abstract": "The review is based on the author\u0027s papers since 1985 in which a new approach\nto the separation of variables (\\SoV) has being developed. It is argued that\n\\SoV, understood generally enough, could be the most universal tool to solve\nintegrable models of the classical and quantum mechanics. It is shown that the\nstandard construction of the action-angle variables from the poles of the\nBaker-Akhiezer function can be interpreted as a variant of \\SoV, and moreover,\nfor many particular models it has a direct quantum counterpart. The list of the\nmodels discussed includes XXX and XYZ magnets, Gaudin model, Nonlinear\nSchr\\\"odinger equation, $SL(3)$-invariant magnetic chain. New results for the\n3-particle quantum Calogero-Moser system are reported.",
"arxiv_id": "solv-int/9504001",
"authors": [
"E. K. Sklyanin"
],
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"solv-int",
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"doi": "10.1143/PTPS.118.35",
"journal_ref": "Prog.Theor.Phys.Suppl.118:35-60,1995",
"title": "Separation of Variables. New Trends.",
"url": "https://arxiv.org/abs/solv-int/9504001"
},
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