2018/02/01 by Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Mathematics · Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Casimir effect #Constructive #Homogeneous space #Integrable system #Kepler problem #Metric (unit) #Minkowski space #Nonlinear Waves and Solitons #Polynomial #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.1088/1742-6596/965/1/012018
published as Journal of Physics: Conference Series 965 (2018), 012018 · 12 pages
openalex publication_date 2018/02/01 · arxiv created 2018/02/19 · openalex created_date 2018/03/06 · arxiv updated 2018/03/14 · openalex updated_date 2026/08/05
Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.