Non-commutative oscillator with Kepler-type dynamical symmetry
High Energy Physics - Theory
2014-11-21 v3 Mathematical Physics
math.MP
Classical Physics
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).
Keywords
Cite
@article{arxiv.1006.1861,
title = {Non-commutative oscillator with Kepler-type dynamical symmetry},
author = {P. M. Zhang and P. A. Horvathy and J. -P. Ngome},
journal= {arXiv preprint arXiv:1006.1861},
year = {2014}
}
Comments
10 pages, 3 figures. Published version