Loop space representation of quantum general relativity

1990/02/01 by Carlo Rovelli, Lee Smolin · 35 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Diffeomorphism #General relativity #Hamiltonian constraint #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Poisson bracket #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics

paper · doi:10.1016/0550-3213(90)90019-a

crossref issued 1990/02/01 · crossref published 1990/02/01 · crossref published-print 1990/02/01 · openalex publication_date 1990/02/01 · crossref created 2002/11/12 · crossref deposited 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/20 · crossref indexed 2026/07/09

Citations

• The Principles of Quantum Mechanics
• Generalized Hamiltonian Dynamics
• Knot Theory and Quantum Gravity
• Quantum field theory and the Jones polynomial
• Fixation of Coordinates in the Hamiltonian Theory of Gravitation
• Exact equation for the loop average in multicolor QCD
• New Variables for Classical and Quantum Gravity
• State models and the jones polynomial
• Dynamical Structure and Definition of Energy in General Relativity

Cited by

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• Quantum aspects of 2+1 gravity
• Non-covariance of the generalized holonomies: Examples
• SU(2) QCD in the path representation: General formalism and Mandelstam identities
• Knot theory and a physical state of quantum gravity
• Fock representations fromU(1)holonomy algebras
• Polymer quantization of the free scalar field and its classical limit
• A new approach to study energy-dependent arrival delays on photons from astrophysical sources
• Semiclassical Loop Quantum Black Hole
• LOOP EQUATIONS IN ABELIAN GAUGE THEORIES
• Loop quantum gravity: an outside view
• Complete LQG propagator: Difficulties with the Barrett-Crane vertex
• Quantum Geometry and Black Hole Entropy
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Reality Conditions and Ashtekar Variables: a Different Perspective
• Loop-Quantum-Gravity Vertex Amplitude
• Minkowski vacuum in background independent quantum gravity
• Effective constraints of loop quantum gravity
• On loop states in loop-quantum gravity
• Knots and classical 3-geometries
• The (2 + 1)-dimensional black hole
• Factor ordering and large-volume dynamics in quantum cosmology
• Flat spacetime vacuum in loop quantum gravity
• Scaling-Based Quantization of Spacetime Microstructure
• The diffeomorphism constraint operator in loop quantum gravity
• Loop Quantum Gravity: An Inside View
• Squeezed vacua in loop quantum gravity
• New scalar constraint operator for loop quantum gravity
• On spectral triples in quantum gravity: I
• Loop states in lattice gauge theory
• Loop quantum gravity [wikipedia]