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Title: Noncommuting spherical coordinates

Abstract

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.

Authors:
 [1]
  1. Department of Physics and Astronomy, University of California, Irvine, California 92697-4575 (United States)
Publication Date:
OSTI Identifier:
20705553
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 70; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.70.087702; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; ANGULAR MOMENTUM; BOUND STATE; CARTESIAN COORDINATES; CHARGED PARTICLES; COMMUTATORS; ENERGY LEVELS; GEOMETRY; MAGNETIC MONOPOLES; MATHEMATICAL SOLUTIONS; POTENTIALS; QUANTUM ELECTRODYNAMICS

Citation Formats

Bander, Myron. Noncommuting spherical coordinates. United States: N. p., 2004. Web. doi:10.1103/PhysRevD.70.087702.
Bander, Myron. Noncommuting spherical coordinates. United States. https://doi.org/10.1103/PhysRevD.70.087702
Bander, Myron. 2004. "Noncommuting spherical coordinates". United States. https://doi.org/10.1103/PhysRevD.70.087702.
@article{osti_20705553,
title = {Noncommuting spherical coordinates},
author = {Bander, Myron},
abstractNote = {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.},
doi = {10.1103/PhysRevD.70.087702},
url = {https://www.osti.gov/biblio/20705553}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 70,
place = {United States},
year = {Fri Oct 15 00:00:00 EDT 2004},
month = {Fri Oct 15 00:00:00 EDT 2004}
}