Embedding of the Racah algebra \(R(n)\) and superintegrability
From MaRDI portal
Publication:2660922
DOI10.1016/j.aop.2021.168397zbMath1457.37077arXiv2010.12822OpenAlexW3093717429MaRDI QIDQ2660922
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
Publication date: 31 March 2021
Published in: Annals of Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.12822
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)
Related Items (11)
Generalized quadratic commutator algebras of PBW-type ⋮ Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras ⋮ Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series ⋮ Coalgebra symmetry for discrete systems ⋮ Representations of the rank two Racah algebra and orthogonal multivariate polynomials ⋮ Unnamed Item ⋮ Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras ⋮ Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators ⋮ N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N) ⋮ Racah algebra R(n) from coalgebraic structures and chains of R(3) substructures ⋮ Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
Cites Work
- Superintegrability in two dimensions and the Racah-Wilson algebra
- From ordinary to discrete quantum mechanics: the Charlier oscillator and its coalgebra symmetry
- Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere
- Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential
- Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
- Superintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopoles
- Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
- \(N\)-dimensional classical integrable systems from Hopf algebras
- The generic quantum superintegrable system on the sphere and Racah operators
- Superintegrable generalizations of the Kepler and Hook problems
- Classical and quantum higher order superintegrable systems from coalgebra symmetry
- Classical and quantum superintegrability with applications
- Recurrence approach and higher rank cubic algebras for theN-dimensional superintegrable systems
- Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
- Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory
- Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform
- Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory
- Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems
- A new family ofNdimensional superintegrable double singular oscillators and quadratic algebraQ(3) ⨁so(n)⨁so(N-n)
- A new superintegrable Hamiltonian
- Maximal superintegrability of the generalized Kepler–Coulomb system onN-dimensional curved spaces
- Group theory of the Smorodinsky–Winternitz system
- A systematic construction of completely integrable Hamiltonians from coalgebras
- Quantum superintegrable system with a novel chain structure of quadratic algebras
- Bargmann and Barut-Girardello models for the Racah algebra
- Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry
- Quantum integrals from coalgebra structure
- Quadratic algebra structure and spectrum of a new superintegrable system inN-dimension
- Wilson polynomials and the generic superintegrable system on the 2-sphere
- Three-Dimensional Isotropic Harmonic Oscillator and SU3
- Superintegrable systems with spin induced by co-algebra symmetry
- The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres
This page was built for publication: Embedding of the Racah algebra \(R(n)\) and superintegrability
