Generalized five-dimensional Kepler system, Yang-Coulomb monopole, and Hurwitz transformation

DOI10.1063/1.3684955zbMath1274.81088arXiv1109.4672OpenAlexW3102557714MaRDI QIDQ2861722

Ian Marquette

Publication date: 11 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4672

zbMATH Keywords

Casimir operatorSmorodinsky-Winternitz type

Mathematics Subject Classification ID

Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (10)

Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang-Coulomb monopole interaction ⋮ Algebraic structure underlying spherical, parabolic, and prolate spheroidal bases of the nine-dimensional MICZ–Kepler problem ⋮ Recurrence approach and higher order polynomial algebras for superintegrable monopole systems ⋮ Dirac equation with anisotropic oscillator, quantum E3′ and Holt superintegrable potentials and relativistic generalized Yang–Coulomb monopole system ⋮ Variables separation and superintegrability of the nine-dimensional MICZ-Kepler problem ⋮ Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras ⋮ Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras ⋮ Massless geodesics in \(\text{AdS}_5\times Y(p,q)\) as a superintegrable system ⋮ Parabolic, prolate spheroidal bases and relation between bases of the nine-dimensional MICZ-Kepler problem ⋮ Exact analytical solutions of the Schrödinger equation for the nine-dimensional MICZ-Kepler problem

Cites Work

• Non-commutative oscillator with Kepler-type dynamical symmetry
• Some ring-shaped potentials as a generalized 4-D isotropic oscillator. Periodic orbits
• The \(su(1,1)\) dynamical algebra for the generalized MICZ-Kepler problem from the Schrödinger factorization
• Hurwitz transformation and oscillator representation of a 5D ``isospin particle
• Bases and interbasis transformations for the \(SU(2)\) monopole
• Superintegrable systems: Polynomial algebras and quasi-exactly solvable Hamiltonians
• Coulomb-oscillator duality in spaces of constant curvature
• Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems
• THE FIVE-DIMENSIONAL KEPLER PROBLEM AS AN SU(2) GAUGE SYSTEM: ALGEBRAIC CONSTRAINT QUANTIZATION
• Generalized Kaluza–Klein monopole, quadratic algebras and ladder operators
• MICZ-Kepler problems in all dimensions
• SUPERSYMMETRIC QUANTUM MECHANICAL GENERALIZED MIC–KEPLER SYSTEM
• Quantum superintegrable systems with quadratic integrals on a two dimensional manifold
• Superintegrability and higher order polynomial algebras
• Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials
• Curved manifolds with conserved Runge–Lenz vectors
• A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
• Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials
• Exact solution of the Schrödinger equation with noncentral parabolic potentials
• Generalized deformed oscillator and nonlinear algebras
• Group theory of the Smorodinsky–Winternitz system
• Nonlinear symmetry algebra of the MIC-Kepler problem on the sphereS³
• 8D oscillator and 5D Kepler problem: The case of nontrivial constraints
• Dynamical O(4) symmetry in the asymptotic field of the Prasad-Sommerfield monopole
• The generalized MIC-Kepler system
• SO(6,2) dynamical symmetry of theSU(2) MIC-Kepler problem
• Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
• Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
• Quadratic algebra approach to relativistic quantum Smorodinsky–Winternitz systems
• Perturbation theory of Kepler motion based on spinor regularization.

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