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

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

2008-06-11

arxiv.org/abs/0806.1808v1

Physics

High Energy Physics

High Energy Physics - Theory

12+1 pages, no figs, LaTeX2e

Scientific paper

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.

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