dorsal/arxiv
View SchemaSeparation of variables for the Ruijsenaars system
| Authors | V. B. Kuznetsov, F. W. Nijhoff, E. K. Sklyanin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9701004 |
| URL | https://arxiv.org/abs/solv-int/9701004 |
| DOI | 10.1007/s002200050231 |
| Journal | Commun.Math.Phys. 189(1997) 855-877 |
Abstract
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax matrix. Two different normalisations of the BA functions are analysed. The canonicity of the separated variables is verified with the use of r-matrix technique. The explicit expressions for the generating function of the separating canonical transform are given in the simplest cases n=2 and n=3. Taking nonrelativistic limit we also construct a separation of variables for the elliptic Calogero-Moser system.
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"abstract": "We construct a separation of variables for the classical n-particle\nRuijsenaars system (the relativistic analog of the elliptic Calogero-Moser\nsystem). The separated coordinates appear as the poles of the properly\nnormalised eigenvector (Baker-Akhiezer function) of the corresponding Lax\nmatrix. Two different normalisations of the BA functions are analysed. The\ncanonicity of the separated variables is verified with the use of r-matrix\ntechnique. The explicit expressions for the generating function of the\nseparating canonical transform are given in the simplest cases n=2 and n=3.\nTaking nonrelativistic limit we also construct a separation of variables for\nthe elliptic Calogero-Moser system.",
"arxiv_id": "solv-int/9701004",
"authors": [
"V. B. Kuznetsov",
"F. W. Nijhoff",
"E. K. Sklyanin"
],
"categories": [
"solv-int",
"hep-th",
"math.QA",
"nlin.SI",
"q-alg"
],
"doi": "10.1007/s002200050231",
"journal_ref": "Commun.Math.Phys. 189(1997) 855-877",
"title": "Separation of variables for the Ruijsenaars system",
"url": "https://arxiv.org/abs/solv-int/9701004"
},
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