Quantum Many--Body Problems and Perturbation Theory
High Energy Physics - Theory
2009-11-07 v1
Abstract
We show that the existence of algebraic forms of exactly-solvable and 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.
Keywords
Cite
@article{arxiv.hep-th/0108160,
title = {Quantum Many--Body Problems and Perturbation Theory},
author = {Alexander V. Turbiner},
journal= {arXiv preprint arXiv:hep-th/0108160},
year = {2009}
}
Comments
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