The structure of invariants in conformal mechanics
arXiv:1402.2288 · doi:10.1016/j.nuclphysb.2014.07.008
Abstract
We investigate the integrals of motion of general conformal mechanical systems with and without confining harmonic potential as well as of the related angular subsystems, by employing the SL(2,R) algebra and its representations. In particular, via the tensor product of two representations we construct new integrals of motion from old ones. Furthermore, the temporally periodic observables (including the integrals) of the angular subsystem are explicitly related to those of the full system in a confining harmonic potential. The techniques are illustrated for the rational Calogero models and their angular subsystems, where they generalize known methods for obtaining conserved charges beyond the Liouville ones.
15 pages
References in corpus (9)
- Physics and Mathematics of Calogero particles
- Self-isospectrality, special supersymmetry, and their effect on the band structure
- Hidden supersymmetry in quantum bosonic systems
- Supersymmetric Calogero models by gauging
- Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
- Calogero models and nonlocal conformal transformations
- Nonlinear supersymmetry in the quantum Calogero model
- Particle dynamics on AdS_2 x S^2 background with two-form flux
- Particle dynamics near extreme Kerr throat and supersymmetry
Cited by in corpus (11)
- On Dunkl angular momenta algebra
- Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
- Runge-Lenz vector in Calogero-Coulomb problem
- Spherical Calogero model with oscillator/Coulomb potential: quantum case
- 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
- Spherical Calogero model with oscillator/Coulomb potential: classical case
- Lobachevsky geometry in TTW and PW systems
- Dunkl symplectic algebra in generalized Calogero models
- Dynamical symmetries of the Calogero-Coulomb model
- Superintegrable deformations of oscillator and Coulomb systems