Quantum Many--Body Problems and Perturbation Theory

Abstract

We show that the existence of algebraic forms of exactly-solvable $A-B-C-D$ and $G_2,F_4$ Olshanetsky-Perelomov Hamiltonians allow to develop the {\it 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.

21 pages, based on 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

References in corpus (2)

• Solvability of the $F_4$ Integrable System
• Canonical Discretization. I. Discrete faces of (an)harmonic oscillator

Cited by in corpus (1)

• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations