Explicit solutions of the classical Calogero & Sutherland systems for any root system
High Energy Physics - Theory
2009-11-11 v1 Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalises the well-known results by Olshanetsky and Perelomov for the A type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.
Keywords
Cite
@article{arxiv.hep-th/0510035,
title = {Explicit solutions of the classical Calogero & Sutherland systems for any root system},
author = {R. Sasaki and K. Takasaki},
journal= {arXiv preprint arXiv:hep-th/0510035},
year = {2009}
}
Comments
18 pages, LaTeX, no figure