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arXiv · 1005.0464

Action-angle variables for dihedral systems on the circle

Olaf Lechtenfeld·Armen Nersessian·Vahagn Yeghikyan
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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.

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Olaf Lechtenfeld, Armen Nersessian, Vahagn Yeghikyan. 2010-05-04. Action-angle variables for dihedral systems on the circle. https://doi.org/10.1016/j.physleta.2010.09.047

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