Quantum Many--Body Problems and Perturbation Theory

Alexander V. Turbiner

doi:10.1134/1.1490123

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arXiv · hep-th/0108160

Quantum Many--Body Problems and Perturbation Theory

Alexander V. Turbiner

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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.

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Alexander V. Turbiner. 2001-08-22. Quantum Many--Body Problems and Perturbation Theory. https://doi.org/10.1134/1.1490123

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