The Poisson realization of $\mathfrak {so}(2, 2k+2)$so(2,2k+2) on magnetic leaves and generalized MICZ-Kepler problems

DOI10.1063/1.4807423zbMath1292.81084arXiv1211.5992OpenAlexW3122536001WikidataQ60132244 ScholiaQ60132244MaRDI QIDQ5402246

Guowu Meng

Publication date: 6 March 2014

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

Full work available at URL: https://arxiv.org/abs/1211.5992

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of differential geometry to physics (53Z05) Two-body problems (70F05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Poisson algebras (17B63) Geometric quantization (53D50) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

Related Items (6)

The classical dynamic symmetry for the Sp(1)-Kepler problems ⋮ Magnetized Kepler manifolds and their quantization ⋮ The classical dynamic symmetry for the \(\mathrm{U}(1)\)-Kepler problems ⋮ MICZ-Kepler systems in noncommutative space and duality of force laws ⋮ Particle motion in generalized Dirac’s monopoles of dimension 2k + 1 ⋮ Hamilton-Dirac systems for charged particles in gauge fields

Cites Work

• Unnamed Item
• The universal Kepler problem
• The geometry of the SU(2) Kepler problem
• Generalized Dirac monopoles in non-Abelian Kaluza--Klein theories
• Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
• A universal phase space for particles in Yang-Mills fields
• Euclidean Jordan algebras, hidden actions, and J-Kepler problems
• Lorentz group and oriented McIntosh-Cisneros-Zwanziger-Kepler orbits
• MICZ-Kepler problems in all dimensions
• Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field
• Reduction in stages and complete quantization of the MIC-Kepler problem

This page was built for publication: The Poisson realization of $\mathfrak {so}(2, 2k+2)$so(2,2k+2) on magnetic leaves and generalized MICZ-Kepler problems