Poisson structure on a space with linear SU(2) fuzziness

Abstract

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum, as well as the Euler parameterization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally-invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

12+1 pages, no figs, LaTeX2e

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Cited by in corpus (7)

• Quantum mechanics on space with SU(2) fuzziness
• Statistical mechanics of free particles on space with Lie type noncommutativity
• Closedness of orbits in a space with SU(2) Poisson structure
• Dirac theory on a space with linear Lie type fuzziness
• Gauge theory on a space with linear Lie type fuzziness
• Central force problem in space with SU(2) Poisson structure
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness