Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-13
J.Phys.A29:2779-2804,1996
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, latex, no figures, Proposition 12 corrected
Scientific paper
10.1088/0305-4470/29/11/014
Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric 3-particle Ruijsenaars model (relativistic generalization of Calogero-Moser-Sutherland model). In the quantum case, an integral operator M is constructed from the Askey-Wilson contour integral. The operator M transforms the eigenfunctions of the commuting Hamiltonians (Macdonald polynomials for the root sytem A2) into the factorized form S(y1)S(y2) where S(y) is a Laurent polynomial of one variable expressed in terms of the 3phi2(y) basic hypergeometric series. The inversion of M produces a new integral representation for the A2 Macdonald polynomials. We also present some results and conjectures for general n-particle case.
Kuznetsov Vadim B.
Sklyanin Evgueni K.
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