Baecklund transformations and Baxter's Q-operator

Details Baecklund transformations and Baxter's Q-operator Baecklund transformations and Baxter's Q-operator

2000-09-04

arxiv.org/abs/nlin/0009009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages, Latex2e (run 3 times), macros included

Scientific paper

The course of 5 lectures given at the seminar "Integrable Systems: from Classical to Quantum" (Universite de Montreal, Jul 26 -- Aug 6, 1999) contains a detailed comment on the recently discovered (Gaudin-Pasquier, 1992) connection between Baecklund transformations in the theory of classical integrable systems on one hand, and Baxter's Q-operator for quantum integrable systems, on the other hand. We restrict our attention to the systems with finite number of degrees of freedom. Our main illustrative example is the periodic Toda lattice. We present a general construction of Q-operator for models governed by the SL(2)-invariant R-matrix and apply it to our example. We discuss also applications of BT and Q-operators to the separation of variables and theory of special functions.

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