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

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Cited by in corpus (20)

• The quantum angular Calogero-Moser model
• Note on Superintegrability of TTW model
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Integrable generalizations of oscillator and Coulomb systems via action-angle variables
• Invariants of the spherical sector in conformal mechanics
• Conformal mechanics inspired by extremal black holes in d=4
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Action-angle variables for the particle near extreme Kerr throat
• 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"
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Quantum Integrals from Coalgebra Structure
• Lobachevsky geometry in TTW and PW systems
• $\mathcal{P}\mathcal{T}$ deformation of angular Calogero models
• Quantum ring models and action-angle variables
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Action-Angle Variables In Conformal Mechanics
• Superintegrable deformations of oscillator and Coulomb systems
• Euler top and freedom in supersymmetrization of one-dimensional mechanics
• Integrability of the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$