Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3496900· OSTI ID:21476569

Marquette, Ian ^[1]

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1. Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E{sub 3} and its dual, the four-dimensional singular oscillator, in four-dimensional Euclidean space E{sub 4}. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are, in these cases, functions not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S{sup 3} using a quadratic algebra. These results point out also that results and explicit formula for structure functions obtained for quadratic, cubic, and higher order polynomial algebras in the context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles.

• OSTI ID: 21476569
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 10; Other Information: DOI: 10.1063/1.3496900; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
DUALITY
ENERGY SPECTRA
EUCLIDEAN SPACE
FOUR-DIMENSIONAL CALCULATIONS
HAMILTONIANS
HARMONIC OSCILLATORS
INTEGRALS
MAGNETIC MONOPOLES
OSCILLATORS
POLYNOMIALS
STRUCTURE FUNCTIONS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
EQUIPMENT
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MONOPOLES
POSTULATED PARTICLES
QUANTUM OPERATORS
RIEMANN SPACE
SPACE
SPECTRA