On the quantization of the Toda chain
Evan WIlliams Theatre
Peter Hall Building
I will consider the problem of finding the spectrum of the closed Toda and q-Toda chain. For this, I will introduce a Kernel obeying a certain fonctional equation involving the spectrum generating function. It can be solved in perturbation starting from the so called assymptotic Bethe Anzats as a first approximation and the correction involves solving a nonlinear integral equation. In the q-Toda case, an interesting modular transform shows up.
Dr Vincent Pasquier, Institut de Physique Théorique, Saclay