Solvability of $F_4$ quantum integrable systems
Mathematical Physics
2009-11-10 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
It is shown that the rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions are obtained by pure algebraic means. For both systems new variables are introduced in which the Hamiltonian has an algebraic form being also (block)-triangular. These variables are a certain invariants of the Weyl group. Both Hamiltonians preserve the same (minimal) flag of spaces of polynomials, which is found explicitly.
Keywords
Cite
@article{arxiv.math-ph/0309025,
title = {Solvability of $F_4$ quantum integrable systems},
author = {Juan C. Lopez Vieyra and Alexander Turbiner},
journal= {arXiv preprint arXiv:math-ph/0309025},
year = {2009}
}
Comments
7 pages, LaTeX, submitted to Proceedings of the 12th International Colloquium Quantum Group and Integrable Systems, Prague, 12-14 June, 2003