Quantum Many--Body Problems and Perturbation Theory

Details Quantum Many--Body Problems and Perturbation Theory Quantum Many--Body Problems and Perturbation Theory

2001-08-22

arxiv.org/abs/hep-th/0108160v1

Phys.Atom.Nucl. 65 (2002) 1135-1143; Yad.Fiz. 65 (2002) 1168-1176

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, based on talks at XXIII Conference `Group-Theoretical Methods in Physics', 31.7 - 5.8.2000, Dubna, Russia and at Wor

Scientific paper

10.1134/1.1490123

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.

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