Noncommuting spherical coordinates

Details Noncommuting spherical coordinates Noncommuting spherical coordinates

2004-07-20

arxiv.org/abs/hep-th/0407177v1

Phys.Rev. D70 (2004) 087702

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, RevTex4 file

Scientific paper

10.1103/PhysRevD.70.087702

Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a magnetic monopole. Restricting the dynamics to the lowest energy level results in noncommutativity for angular variables and to a definition of a noncommuting spherical product. The values of the commutators of various angular variables are not arbitrary but are restricted by the discrete magnitude of the magnetic monopole charge. An algebra, isomorphic to angular momentum, appears. This algebra is used to define a spherical star product. Solutions are obtained for dynamics in the presence of additional angular dependent potentials.

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