Central force problem in space with SU(2) Poisson structure
arXiv:1312.2115 · doi:10.1007/JHEP07(2013)022
Abstract
The central force problem is considered in a three dimensional space in which the Poisson bracket among the spatial coordinates is the one by the SU(2) Lie algebra. It is shown that among attractive power-law potentials it is only the Kepler one that all of its bound-states make closed orbits. The analytic solution of the path equation under the Kepler potential is presented. It is shown that except the Kepler potential, in contrast to ordinary space, all of the potentials for which all of the almost circular orbits are closed are non-power-law ones. For the non-power-law potentials examples of the numerical solutions of the path equations are presented.
18 pages, 6 figs
References in corpus (8)
- Newton's Equation on the kappa space-time and the Kepler problem
- The Energy-momentum of a Poisson structure
- Field theories on spaces with linear fuzziness
- Field theory amplitudes in a space with SU(2) fuzziness
- Loop diagrams in space with SU(2) fuzziness
- Quantum mechanics on space with SU(2) fuzziness
- Thermodynamics on Fuzzy Spacetime
- Dirac theory on a space with linear Lie type fuzziness