Separation of variables for the ? Ruijsenaars model and a new integral representation for the ? Macdonald polynomials
Abstract
Using the Baker - Akhiezer function technique we construct a separation of variables for the classical trigonometric three-particle Ruijsenaars model (a relativistic generalization of the 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 (the Macdonald polynomials for the root sytem 0305-4470/29/11/014/img7) into the factorized form 0305-4470/29/11/014/img8 where S(y) is a Laurent polynomial of one variable expressed in terms of the 0305-4470/29/11/014/img9 basic hypergeometric series. The inversion of M produces a new integral representation for the 0305-4470/29/11/014/img7 Macdonald polynomials. We also present some results and conjectures for the general n-particle case.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- June 1996
- DOI:
- 10.1088/0305-4470/29/11/014
- arXiv:
- arXiv:q-alg/9602023
- Bibcode:
- 1996JPhA...29.2779K
- Keywords:
-
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Mathematics - Classical Analysis and ODEs;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 31 pages, latex, no figures, Proposition 12 corrected