Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals
Exactly Solvable and Integrable Systems
2013-08-30 v1 Mathematical Physics
math.MP
Abstract
We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.
Keywords
Cite
@article{arxiv.1209.1314,
title = {Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals},
author = {V. Ayadi and L. Feher and T. F. Gorbe},
journal= {arXiv preprint arXiv:1209.1314},
year = {2013}
}
Comments
Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 pages