Geometric quantization of the \(1:1\) oscillator

DOI10.1007/s12346-020-00417-xzbMath1452.81120OpenAlexW3082012093MaRDI QIDQ2006997

Richard H. Cushman, Jędrzej Śniatycki

Publication date: 12 October 2020

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-020-00417-x

zbMATH Keywords

Bohr-Sommerfeld-Heisenberg quantization\(\mathrm{SU}(2)\) representation2d-harmonic oscillator

Mathematics Subject Classification ID

Hamilton's equations (70H05) Geometry and quantization, symplectic methods (81S10) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Coadjoint orbits; nilpotent varieties (17B08) Canonical quantization (81S08)

Cites Work

• On Bohr-Sommerfeld-Heisenberg quantization
• Geometric quantization and quantum mechanics
• Differential Geometry of Singular Spaces and Reduction of Symmetry
• Global Aspects of Classical Integrable Systems

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