Quantum Many–Body Problems and Perturbation Theory
نویسنده
چکیده
We show that the existence of algebraic forms of exactly-solvable A−B− C−D and G2, F4 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure algebraic means. A classification of perturbations leading to such a perturbation theory based on representation theory of Lie algebras is given. In particular, this scheme admits an explicit study of anharmonic many-body problems. Some examples are presented. Based on invited talks at XXIII Conference ‘Group-Theoretical Methods in Physics’, 31.7 5.8.2000, Dubna, Russia and at Workshop ‘Calogero model: thirty years after’, 24-27.5.2001, Rome, Italy [email protected], [email protected] On leave of absence from the Institute for Theoretical and Experimental Physics, Moscow 117259, Russia.
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