Refined algebraic quantization in the oscillator representation of SL(2, ℝ)

DOI10.1063/1.533126zbMath0981.81042arXivgr-qc/9907004OpenAlexW3101857519MaRDI QIDQ2737809

Jorma Louko, Carlo Rovelli

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/gr-qc/9907004

zbMATH Keywords

reduced phase spaceconstrained Hamiltonian systemnon-Hausdorff topologygroup averagingAshtekar's algebraic quantizationgauge group \(\text{SL}(2, \mathbb{R})\)Isham's group theoretic quantizationunreduced phase space

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10)

Related Items (10)

Group averaging in the (p,q) oscillator representation of SL(2,R) ⋮ Can chaos be observed in quantum gravity? ⋮ REFINED ALGEBRAIC QUANTIZATION WITH THE TRIANGULAR SUBGROUP OFSL(2, ℝ) ⋮ Group theoretical quantization and the example of a phase space S1×R+ ⋮ Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions ⋮ Deformation quantization of constrained systems: a group averaging approach ⋮ Supergravity on a three-torus: quantum linearization instabilities with a supergroup ⋮ Loop quantum cosmology of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>FRW models ⋮ The \(\mathrm{SL}(2,\mathbb R)\) totally constrained model: three quantization approaches ⋮ Constraint rescaling in refined algebraic quantisation: Momentum constraint

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