2010/06/30 by Pengming Zhang, P. M. Zhang, P. A. Horváthy +3 · 20 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Bound state #Commutative property #Dirac (video compression format) #Ellipse #Geometry #Kepler problem #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #hep-th #math-ph #math.MP #physics.class-ph
paper · pdf · doi:10.1016/j.physleta.2010.08.054
published in Physics Letters A 374(42), 4275-4278 (Elsevier BV) · 10 pages, 3 figures. Published version
openalex publication_date 2010/08/22 · arxiv created 2010/09/10 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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).