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 the 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 the nonrelativistic limit we also construct a separation of variables for the elliptic Calogero-Moser system.
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Received: 10 January 1997 / Accepted: 1 April 1997
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Kuznetsov, V., Nijhoff, F. & Sklyanin, E. Separation of Variables for the Ruijsenaars System . Comm Math Phys 189, 855–877 (1997). https://doi.org/10.1007/s002200050231
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DOI: https://doi.org/10.1007/s002200050231