Perturbations of integrable systems and Dyson-Mehta integrals

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dc.creatorTurbiner, Alexander
dc.date2003-09-10
dc.date.accessioned2026-07-07T04:15:43Z
dc.date.available2026-07-07T04:15:43Z
dc.descriptionWe 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.
dc.description17pp, LaTeX, to be published in Proceedings of the Workshop "Superintegrable systems in classical and quantum mechanics", Montreal, Canada, September, 2002; CRM Press
dc.identifierhttps://arxiv.org/abs/hep-th/0309109
dc.identifierhttp://arxiv.org/abs/hep-th/0309109
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52115
dc.subjectHigh Energy Physics - Theory
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.titlePerturbations of integrable systems and Dyson-Mehta integrals
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