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 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.

8 pages; v2: references added, typos fixed, version for PLA

References in corpus (4)

• N=4 superconformal Calogero models
• Calogero models and nonlocal conformal transformations
• N=4 supersymmetric 3-particles Calogero model
• A New Look at the Quantum Mechanics of the Harmonic Oscillator

Cited by in corpus (8)

• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Near-horizon dynamics of particle in extreme Reissner-Nordström and Clément-Gal'tsov black hole backgrounds: action-angle variables
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Quantum Integrals from Coalgebra Structure
• $\mathcal{P}\mathcal{T}$ deformation of angular Calogero models
• Action-Angle Variables In Conformal Mechanics
• Superintegrable deformations of oscillator and Coulomb systems