Action-angle variables for dihedral systems on the circle
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 I2(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 A2, BC2 and G2 three-particle rational Calogero models on R, which we also analyze.
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