Perturbations of integrable systems and Dyson-Mehta integrals
Abstract
Description
We show that the existence of algebraic forms of quantum, exactly-solvable, completely-integrable $A-B-C-D$ and $G_2, F_4, E_{6,7,8}$ Olshanetsky-Perelomov Hamiltonians allow to develop the {\it algebraic} perturbation theory, where corrections are computed by pure linear algebra means. A Lie-algebraic classification of such perturbations is given. In particular, this scheme admits an explicit study of anharmonic many-body problems. The approach also allows to calculate the ratios of a certain generalized Dyson-Mehta integrals algebraically, which are interested by themselves.
17pp, LaTeX, to be published in Proceedings of the Workshop "Superintegrable systems in classical and quantum mechanics", Montreal, Canada, September, 2002; CRM Press
17pp, LaTeX, to be published in Proceedings of the Workshop "Superintegrable systems in classical and quantum mechanics", Montreal, Canada, September, 2002; CRM Press