Strict quantization of coadjoint orbits

DOI10.1063/1.532644zbMath0986.81057arXivmath-ph/9807027OpenAlexW2081090559MaRDI QIDQ4701566

Nicolaas P. Landsman

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/math-ph/9807027

zbMATH Keywords

\(C^*\)-algebradeformation quantizationcompact symplectic manifoldcompact connected Lie groupquantization mapsstrict quantizationintegral coadjoint orbit

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Applications of selfadjoint operator algebras to physics (46L60) Coherent states (81R30) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55) Operator algebra methods applied to problems in quantum theory (81R15) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (13)

Order-unit quantum Gromov--Hausdorff distance ⋮ Open strings in Lie groups and associative products ⋮ Poisson boundary of the dual of \(\text{SU}_q(n)\). ⋮ Some continuous field quantizations, equivalent to the \(C^*\)-Weyl quantization ⋮ QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS ⋮ Deformation quantization and homological reduction of a lattice gauge model ⋮ Cotangent bundles for ``matrix algebras converge to the sphere ⋮ Dirac operators for matrix algebras converging to coadjoint orbits ⋮ Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras ⋮ Unnamed Item ⋮ Weyl quantization for semidirect products ⋮ Coadjoint Orbits of Certain Motion Groups and Their Coherent States ⋮ Properties of states on Weyl algebra with variable multiplication law

Cites Work

• General concept of quantization
• Strict deformation quantization of a particle in external gravitational and Yang-Mills fields
• The classical limit of quantum partition functions
• Quantization of equivariant vector bundles
• Deformation quantization of Heisenberg manifolds
• Operations on continuous bundles of \(C^*\)-algebras
• The classical limit of quantum spin systems
• Coherent states for arbitrary Lie group
• Classical and thermodynamic limits for generalised quantum spin systems
• Realization of compact Lie algebras in Kahler manifolds
• Quantization and unitary representations

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