Group theoretical quantization and the example of a phase space S1×R+

DOI10.1063/1.533258zbMath0987.81044arXivquant-ph/9908079OpenAlexW1493527796MaRDI QIDQ2737951

Martin Bojowald, Thomas Strobl

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/quant-ph/9908079

zbMATH Keywords

symplectic manifoldsprojection methodadmissible group actionsquantize gravitysubbundles of cotangent spacestwo-dimensional prototypes

Mathematics Subject Classification ID

Quantization of the gravitational field (83C45) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Geometry and quantization, symplectic methods (81S10) Momentum maps; symplectic reduction (53D20) Geometric quantization (53D50)

Related Items (5)

Group averaging in the (p,q) oscillator representation of SL(2,R) ⋮ Quantization of the zigzag model ⋮ REFINED ALGEBRAIC QUANTIZATION WITH THE TRIANGULAR SUBGROUP OFSL(2, ℝ) ⋮ Refined algebraic quantization in the oscillator representation of SL(2, ℝ) ⋮ Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles

Cites Work

• Symplectic cuts
• The Plancherel formula for the universal covering group of SL(R, 2)
• Irreducible unitary representations of the Lorentz group
• Refined algebraic quantization in the oscillator representation of SL(2, ℝ)
• THE FIVE-DIMENSIONAL KEPLER PROBLEM AS AN SU(2) GAUGE SYSTEM: ALGEBRAIC CONSTRAINT QUANTIZATION
• Generalised coherent states and group representations on Hilbert spaces of analytic functions
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
• On the relation between 2+1 Einstein gravity and Chern-Simons theory

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