Action-angle variables for dihedral systems on the circle
High Energy Physics - Theory
2011-01-18 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and establish a local equivalence with a free particle on the circle. We perform the quantization of these systems in the action-angle variables and discuss the supersymmetric extension of this procedure. By allowing radial motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2 three-particle rational Calogero models on R, which we also analyze.
Cite
@article{arxiv.1005.0464,
title = {Action-angle variables for dihedral systems on the circle},
author = {Olaf Lechtenfeld and Armen Nersessian and Vahagn Yeghikyan},
journal= {arXiv preprint arXiv:1005.0464},
year = {2011}
}
Comments
8 pages; v2: references added, typos fixed, version for PLA