Canonical Quantum Gravity

Abstract

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical theory as I can by pictorial visualization. Algebraic aspects dominate my description of the quantization program. I address the problem of observables. The reader is encouraged to follow the broad outlines and not worry about the technical details.

Latex, 35 pages. arXiv admin note: figures missing

Cited by in corpus (68)

• Background Independent Quantum Gravity: A Status Report
• Partial observables
• Forks in the Road, on the Way to Quantum Gravity
• Structural Issues in Quantum Gravity
• Relational Observables in Gravity: a Review
• The Superspace of Geometrodynamics
• The Rest-Frame Instant Form of Metric Gravity
• Beables/Observables in Classical and Quantum Gravity
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Quantum geometrodynamics: whence, whither?
• Change in Hamiltonian General Relativity from the Lack of a Time-like Killing Vector Field
• Can chaos be observed in quantum gravity?
• A Shape Dynamics Tutorial
• The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
• The role of time in relational quantum theories
• Symmetry and Evolution in Quantum Gravity
• The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory
• Superspace Dynamics and Perturbations Around "Emptiness"
• Reality conditions for Ashtekar variables as Dirac constraints
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
• Jacobi's Principle and the Disappearance of Time
• de Broglie-Bohm Interpretation for the Wave Function of Quantum Black Holes
• Generalized Ashtekar variables for Palatini f(R) models
• Chiral supergravity and anomalies
• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
• Scaling limits of lattice quantum fields by wavelets
• Shape Theory. III. Comparative Theory of Backgound Independence
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Equivalent Theories and Changing Hamiltonian Observables in General Relativity
• A Local Resolution of the Problem of Time. IV. Quantum outline and piecemeal Conclusion
• A Local Resolution of the Problem of Time. IX. Spacetime Constructability
• Geometry from Brackets Consistency
• Chaos, Dirac observables and constraint quantization
• A Local Resolution of the Problem of Time. VII. Constraint Closure
• Chromodynamics and Gravity as Theories on Loop Space
• Quantum Geometrodynamics of the Bianchi IX cosmological model
• Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time
• Quantum spacetime without observers: ontological clarity and the conceptual foundations of quantum gravity
• Ehrenfest's Principle and the Problem of Time in Quantum Gravity
• What Are Observables in Hamiltonian Einstein-Maxwell Theory?
• Problem of Time and Background Independence: classical version's higher Lie Theory
• A Local Resolution of the Problem of Time. XIV. Grounding on Lie's Mathematics
• Evolving Constants of Motion
• Tetrad Gravity: I) A New Formulation
• Progress and Gravity: Overcoming Divisions between General Relativity and Particle Physics and between Physics and HPS
• Spin connection as Lorentz gauge field: propagating torsion
• Nambu variant of Local Resolution of Problem of Time and Background Independence
• General Relativity without paradigm of space-time covariance, and resolution of the problem of time
• General covariance and the objectivity of space-time point-events
• BRST operator quantization of generally covariant gauge systems
• The Dynamics of Relativistic Hypersurfaces
• The Issue of Time in Quantum Geometrodynamics
• Quantum Mechanics for Totally Constrained Dynamical Systems and Evolving Hilbert Spaces
• Change in Hamiltonian General Relativity with Spinors
• Time in Quantum Geometrodynamics
• Diffeomorphism Invariant Theories and Vector Supersymmetry
• Lie Theory suffices to understand, and Locally Resolve, the Problem of Time
• Constraints in Quantum Geometrodynamics
• Quaternion-Loop Quantum Gravity
• World-line observables and clocks in General Relativity
• A note on the Hamiltonian constraint in canonical GR
• WKB approach to the gravity-matter dynamics: a cosmological implementation
• Comparative Theory of Background Independence
• Quantization of the interior of the black hole
• Quantization of a generally covariant gauge system with two super Hamiltonian constraints
• On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook
• A Local Resolution of the Problem of Time. VIII. Assignment of Observables