Action-angle variables for dihedral systems on the circle

DOI10.1016/J.PHYSLETA.2010.09.047zbMATH Open1238.81148arXiv1005.0464OpenAlexW2026606954MaRDI QIDQ418611

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Publication date: 29 May 2012

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1005.0464

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