Non-commutative oscillator with Kepler-type dynamical symmetry
arXiv:1006.1861 · doi:10.1016/j.physleta.2010.08.054
Abstract
A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential, introduced by McIntosh, Cisneros, and by Zwanziger some time ago. The trajectories are (arcs of) ellipses, which, in the commutative limit, reduce to the circular hodographs of the Kepler problem. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and actually extends to the conformal algebra o(4,2).
10 pages, 3 figures. Published version
References in corpus (7)
- Berry Phase Effects on Electronic Properties
- Covariant hamiltonian dynamics
- Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole
- Curved manifolds with conserved Runge-Lenz vectors
- Conserved quantities in non-abelian monopole fields
- Higher order first integrals of motion in a gauge covariant Hamiltonian framework
- Dynamical supersymmetry of spin particle-magnetic field interaction
Cited by in corpus (11)
- Exotic galilean symmetry and non-commutative mechanics
- Generalized five-dimensional Kepler system, Yang-Coulomb monopole and Hurwitz transformation
- Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators
- Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces
- MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
- Closedness of orbits in a space with SU(2) Poisson structure
- MultiCarroll dynamics
- Central force problem in space with SU(2) Poisson structure
- Dirac equation with a magnetic field in 3D non-commutative phase space
- Eigenvalue problem for radial potentials in space with SU(2) fuzziness
- Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism