English

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

R2 v1 2026-07-22T20:08:21.639Z