Completeness of superintegrability in two-dimensional constant-curvature spaces

From MaRDI portal
Publication:2735755

DOI10.1088/0305-4470/34/22/311zbMath0993.70014arXivmath-ph/0102006OpenAlexW1980094194MaRDI QIDQ2735755

Ernest G. Kalnins, Willard jun. Miller, Jonathan M. Kress, George S. Pogosyan

Publication date: 4 September 2001

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

Full work available at URL: https://arxiv.org/abs/math-ph/0102006




Related Items

Cubic first integrals of autonomous dynamical systems in E2 by an algorithmic approachUnified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifoldContraction of broken symmetries via Kac-Moody formalismExact and quasiexact solvability of second order superintegrable quantum systems. II. Relation to separation of variablesBôcher contractions of conformally superintegrable Laplace equationsAn algebraic geometric classification of superintegrable systems in the Euclidean planeHigher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike systemProjectively equivalent 2-dimensional superintegrable systems with projective symmetriesAn integrable Hénon–Heiles system on the sphere and the hyperbolic planeQuadratic algebra contractions and second-order superintegrable systemsSuperintegrability in a two-dimensional space of nonconstant curvatureQuantum superintegrability and exact solvability in n dimensionsComplete sets of invariants for dynamical systems that admit a separation of variablesSuperintegrability with third-order integrals in quantum and classical mechanicsOn harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2. II.Hamiltonians separable in Cartesian coordinates and third-order integrals of motionIntegrable and superintegrable quantum systems in a magnetic fieldRiemann functions and the group E(1,1)Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: Applications to ladder operators and superintegrabilitySymmetries of the hydrogen atom and algebraic familiesElliptic basis for the Zernike system: Heun function solutionsSuperintegrable Anharmonic Oscillators on N-dimensional Curved SpacesCanonoid and Poissonoid transformations, symmetries and biHamiltonian structuresAn algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimensionSuperintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groupsBianchi type-V spinning particle on \(\mathcal{S}^2\)Quantum superintegrable Zernike systemContractions of degenerate quadratic algebras, abstract and geometricKoenigs theorem and superintegrable Liouville metricsNon-Hermitian superintegrable systemsThe anisotropic oscillator on curved spaces: a exactly solvable modelSuperintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separabilityNecessary conditions for super-integrability of Hamiltonian systemsExact solvability of superintegrable Benenti systemsQuantum superintegrable systems with quadratic integrals on a two dimensional manifoldIntertwining symmetry algebras of quantum superintegrable systems on constant curvature spacesLeonard Euler: addition theorems and superintegrable systemsThe harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvatureOn Superintegrable Systems with a Cubic Integral of MotionClassical and quantum superintegrability of Stäckel systemsBôcher and abstract contractions of 2nd order quadratic algebrasSolution of the Dirac equation with some superintegrable potentials by the quadratic algebra approachFrom ordinary to discrete quantum mechanics: the Charlier oscillator and its coalgebra symmetryLaplace-type equations as conformal superintegrable systemsSuperintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentialsSupersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion(Quasi)-exact-solvability on the sphere SnStäckel equivalence of non-degenerate superintegrable systems, and invariant quadricsSpherical geometry, Zernike’s separability, and interbasis expansion coefficientsMassless geodesics in \(\text{AdS}_5\times Y(p,q)\) as a superintegrable systemSuslov problem with the Clebsch-Tisserand potentialCurvature as an Integrable DeformationSuperintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopolesKilling-Yano Tensors and Superintegrable Systems(Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetrySuperintegrable deformations of superintegrable systems: Quadratic superintegrability and higher-order superintegrabilityFrom oscillator(s) and Kepler(s) potentials to general superintegrable systems in spaces of constant curvatureNondegenerate 2D complex Euclidean superintegrable systems and algebraic varietiesCentral potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theorySecond order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transformSecond order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theoryExact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminariesThe quantum free particle on spherical and hyperbolic spaces: A curvature dependent approachA new way to classify 2D higher order quantum superintegrable systemsSuperintegrability of three-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systemsSuperintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S 3 and on the hyperbolic space H 3