Solvability of the G_2 Integrable System
solv-int
2009-10-30 v4 Condensed Matter
High Energy Physics - Theory
Exactly Solvable and Integrable Systems
Abstract
It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.
Keywords
Cite
@article{arxiv.solv-int/9707005,
title = {Solvability of the G_2 Integrable System},
author = {Marcos Rosenbaum and Alexander Turbiner and Antonio Capella},
journal= {arXiv preprint arXiv:solv-int/9707005},
year = {2009}
}
Comments
18 pages, LaTeX, some minor typos corrected