Group averaging in the (p,q) oscillator representation of SL(2,R)

DOI10.1063/1.1689001zbMath1071.81069arXivgr-qc/0312014OpenAlexW3101456991WikidataQ62038304 ScholiaQ62038304MaRDI QIDQ4833398

Alberto Molgado, Jorma Louko

Publication date: 15 December 2004

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

Full work available at URL: https://arxiv.org/abs/gr-qc/0312014

Mathematics Subject Classification ID

Applications of manifolds of mappings to the sciences (58D30) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Geometry and quantization, symplectic methods (81S10) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Constrained dynamics, Dirac's theory of constraints (70H45)

Related Items (6)

REFINED ALGEBRAIC QUANTIZATION WITH THE TRIANGULAR SUBGROUP OFSL(2, ℝ) ⋮ Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions ⋮ Deformation quantization of constrained systems: a group averaging approach ⋮ The \(\mathrm{SL}(2,\mathbb R)\) totally constrained model: three quantization approaches ⋮ Ostrogradski approach for the Regge-Teitelboim type cosmology ⋮ Constraint rescaling in refined algebraic quantisation: Momentum constraint

Cites Work

• Constrained dynamics and quantum gravity
• The BRS method of geometric quantization: Some examples
• On some results of Strichartz and of Rallis and Schiffman
• On the dual pairs \((O(p,q), SL(2,\mathbb{R}))\), \((U(p,q), U(1,1))\) and \((Sp(p,q), O^*(4))\)
• Constrained quantization and \(\theta \)-angles
• Invariant tensors for simple groups
• Rieffel induction as generalized quantum Marsden-Weinstein reduction
• On correspondence of BRST-BFV, Dirac, and refined algebraic quantizations of constrained systems
• ON GROUP AVERAGING FOR SO(n, 1)
• Refined algebraic quantization in the oscillator representation of SL(2, ℝ)
• Group theoretical quantization and the example of a phase space S1×R+
• Survey of two-time physics
• THE FIVE-DIMENSIONAL KEPLER PROBLEM AS AN SU(2) GAUGE SYSTEM: ALGEBRAIC CONSTRAINT QUANTIZATION
• Quantization of the optical phase space in terms of the group
• A uniqueness theorem for constraint quantization
• On the generality of refined algebraic quantization
• Quantum observables and recollapsing dynamics
• An algebraic extension of Dirac quantization: Examples
• Against the Wheeler - DeWitt equation
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• The Phoenix Project: master constraint programme for loop quantum gravity
• Quantum Theory of Gravity. I. The Canonical Theory
• Reduction, quantization, and nonunimodular groups
• Relational evolution of the degrees of freedom of generally covariant quantum theories

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