Coherent states for canonical quantum general relativity and the infinite tensor product extension

2001/02/09 by H. Sahlmann, T. Thiemann, O. Winkler · 12 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Extension (predicate logic) #General relativity #Hilbert space #Limit (mathematics) #Mathematics of general relativity #Noncommutative and Quantum Gravity Theories #Problem of time #Tensor product #Tensor product of Hilbert spaces #Theory of relativity #gr-qc #hep-lat #hep-th #quant-ph

paper · pdf · doi:10.1016/s0550-3213(01)00226-7

published as Nucl.Phys. B606 (2001) 401-440 · 37 p., latex2e, no figures

arxiv created 2001/02/09 · openalex publication_date 2001/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far.

Citations

• Spin Networks in Gauge Theory
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Projective techniques and functional integration for gauge theories
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Nonstandard optics from quantum space-time

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• Quantum Geometry of the Light Cone: Fock representation and Spectrum of Radiated Power
• The Phoenix Project: master constraint programme for loop quantum gravity
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• Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
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