Closedness of orbits in a space with SU(2) Poisson structure

Abstract

The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all of the bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of the motion is also worked out.

20 pages, no fig. arXiv admin note: text overlap with arXiv:1312.2115

References in corpus (9)

• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Newton's Equation on the kappa space-time and the Kepler problem
• 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
• Statistical mechanics of free particles on space with Lie type noncommutativity
• Dirac theory on a space with linear Lie type fuzziness

Cited by in corpus (1)

• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism