Quadratic algebra for superintegrable monopole system in a Taub-NUT space

DOI10.1063/1.4962924zbMath1347.81038arXiv1604.05560OpenAlexW3098822371WikidataQ57999125 ScholiaQ57999125MaRDI QIDQ2825544

Ian Marquette, Md. Fazlul Hoque, Yao-Zhong Zhang

Publication date: 13 October 2016

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

Full work available at URL: https://arxiv.org/abs/1604.05560

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) Atomic physics (81V45) Groups and algebras in quantum theory and relations with integrable systems (81R12) Kaluza-Klein and other higher-dimensional theories (83E15) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Exact solutions to problems in general relativity and gravitational theory (83C15) Motion of charged particles (78A35) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

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Cites Work

• Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential
• Low energy scattering of nonabelian monopoles.
• On extended Taub-NUT metrics
• Models for quadratic algebras associated with second order superintegrable systems in 2D
• Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems
• Classical and quantum superintegrability with applications
• Generalized Kaluza–Klein monopole, quadratic algebras and ladder operators
• Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems
• MICZ-Kepler problems in all dimensions
• A new family ofNdimensional superintegrable double singular oscillators and quadratic algebraQ(3) ⨁so(n)⨁so(N-n)
• SUPERSYMMETRIC QUANTUM MECHANICAL GENERALIZED MIC–KEPLER SYSTEM
• The four-dimensional conformal Kepler problem reduces to the three-dimensional Kepler problem with a centrifugal potential and Dirac’s monopole field. Classical theory
• Generalized deformed oscillator and nonlinear algebras
• Group theory of the Smorodinsky–Winternitz system
• On the interbasis expansion for the Kaluza‐Klein monopole system
• Quantised singularities in the electromagnetic field,
• Nonlinear symmetry algebra of the MIC-Kepler problem on the sphereS³
• The generalized MIC-Kepler system
• Two kinds of generalized Taub-NUT metrics and the symmetry of associated dynamical systems
• On realizations of polynomial algebras with three generators via deformed oscillator algebras
• Quadratic algebra structure and spectrum of a new superintegrable system inN-dimension
• Quantization of the multifold Kepler system