Quadratic algebras for three-dimensional superintegrable systems

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S106377881002002X· OSTI ID:21426779

Daskaloyannis, C; Tanoudis, Y ^[1]

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1. Aristotle University of Thessaloniki, Mathematics Department (Greece)

The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

• OSTI ID: 21426779
• Journal Information: Physics of Atomic Nuclei, Vol. 73, Issue 2; Other Information: DOI: 10.1134/S106377881002002X; Copyright (c) 2010 Pleiades Publishing, Ltd.; ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
HAMILTONIANS
INTEGRALS
POISSON EQUATION
POTENTIALS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL OPERATORS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS