Non-commutative oscillator with Kepler-type dynamical symmetry

Details Non-commutative oscillator with Kepler-type dynamical symmetry Non-commutative oscillator with Kepler-type dynamical symmetry

2010-06-09

arxiv.org/abs/1006.1861v3

Physics Letters A374:4275-4278, 2010

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, 3 figures. Published version

Scientific paper

10.1016/j.physleta.2010.08.054

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).

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