Perturbations of integrable systems and Dyson-Mehta integrals

Alexander Turbiner

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arXiv · hep-th/0309109

Perturbations of integrable systems and Dyson-Mehta integrals

Alexander Turbiner

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Abstract

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.

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hep-th cond-mat.stat-mech math-ph math.MP nlin.SI quant-ph

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Alexander Turbiner. 2003-09-10. Perturbations of integrable systems and Dyson-Mehta integrals. https://arxiv.org/abs/hep-th/0309109

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