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Separation of variables for the Ruijsenaars system

V. B. Kuznetsov·F. W. Nijhoff·E. K. Sklyanin
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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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V. B. Kuznetsov, F. W. Nijhoff, E. K. Sklyanin. 1997-01-10. Separation of variables for the Ruijsenaars system. https://doi.org/10.1007/s002200050231

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