Séminaire de Physique Théorique

Kepler-type symmetries of non-commutative oscillators
Jean-Paul Ngome (LMPT)
Thursday 27 January 2011 14:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
We re-visite Kepler-type motions. Through a dual description in momentum space, we derive 3D non-commutative oscillator, with no kinetic term but with a certain momentum-dependent potential, admitting a conserved Runge-Lenz vector. The latter corresponds to a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential, introduced by McIntosh, Cisneros, and by Zwanziger. 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).

Liens :