Separation of variables for the Ruijsenaars system
solv-int
2009-10-30 v1 High Energy Physics - Theory
Quantum Algebra
Exactly Solvable and Integrable Systems
q-alg
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.
Keywords
Cite
@article{arxiv.solv-int/9701004,
title = {Separation of variables for the Ruijsenaars system},
author = {V. B. Kuznetsov and F. W. Nijhoff and E. K. Sklyanin},
journal= {arXiv preprint arXiv:solv-int/9701004},
year = {2009}
}
Comments
26 pages, LaTex, no figures