On reduction of the four-dimensional harmonic oscillator

DOI10.1063/1.525104zbMath0476.70018OpenAlexW2047249539MaRDI QIDQ3932337

Toshihiro Iwai

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.525104

zbMATH Keywords

four-dimensional harmonic oscillatorreduction of energy surface by a one-parameter subgroupsymmetry group SU(4)symmetry of three-dimensional Kepler problem in the large

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamics of a system of particles, including celestial mechanics (70F99) Applications of Lie groups to the sciences; explicit representations (22E70) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items

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 Hopf fibration and geometric \(\mathrm{SO}(3)\) reduction of the \(4\mathrm{DOF}\) harmonic oscillator, Normalization and the detection of integrability: The generalized van der Waals potential, On a ‘‘conformal’’ Kepler problem and its reduction, Rydberg states of atoms and molecules. Basic group theoretical and topological analysis, Quantization of the conformal Kepler problem and its application to the hydrogen atom, The symmetry group of the harmonic oscillator and its reduction

Cites Work

• Reduction of symplectic manifolds with symmetry
• A general setting for reduction of dynamical systems