Time and a Physical Hamiltonian for Quantum Gravity

2011/08/31 by Viqar Husain, Tomasz Pawłowski, Tomasz Pawlowski · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Hamiltonian (control theory) #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Mechanics and Applications #Quantum gravity #Quantum mechanics #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevlett.108.141301

5 pages, version to appear in Phys. Rev. Lett

arxiv created 2012/02/20 · openalex publication_date 2012/04/05 · arxiv updated 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.

Citations

• Algebraic quantum gravity (AQG): I. Conceptual setup
• Canonical Variables for General Relativity
• Loop quantum cosmology: an overview
• Coherent states for canonical quantum general relativity and the infinite tensor product extension
• Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
• Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
• Universality and scaling in gravitational collapse of a massless scalar field
• Quantum Theory of Gravity. I. The Canonical Theory
• Dust reference frame in quantum cosmology
• Gravity quantized: Loop quantum gravity with a scalar field
• New Hamiltonian formulation of general relativity
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Partial and Complete Observables for Canonical General Relativity
• Partial observables
• Mixmaster Universe

Cited by

• Shock waves in classical dust collapse
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model
• Quantum Geometry of the Light Cone: Fock representation and Spectrum of Radiated Power