Quantum geometrodynamics: whence, whither?

Abstract

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.

25 pages; invited contribution for the Proceedings of the seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, Germany, April 2008

References in corpus (23)

• The Dynamics of General Relativity
• Geometrodynamics of Schwarzschild Black Holes
• Quantum phantom cosmology
• Canonical Quantum Gravity
• Hamiltonian thermodynamics of the Reissner-Nordström-anti-de Sitter black hole
• Quantum cosmology with big-brake singularity
• Wavefunction of a Black Hole and the Dynamical Origin of Entropy
• Wheeler-DeWitt equation and Feynman diagrams
• Cosmological Landscape From Nothing: Some Like It Hot
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Semiclassical approximation to supersymmetric quantum gravity
• Toward a Midisuperspace Quantization of LeMaitre-Tolman-Bondi Collapse Models
• Symmetries, Horizons, and Black Hole Entropy
• Why there is something rather than nothing (out of everything)?
• Quantum theory of gravitational collapse (lecture notes on quantum conchology)
• Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity
• Quantum Cosmological Models
• Symmetries,Singularities and the De-Emergence of Space
• Hawking temperature from quasi-normal modes
• The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
• Solution of quantum Dirac constraints via path integral
• Quantum Dirac constraints, Ward identities and path integral in relativistic gauge
• Quantum gravitational effects in de Sitter space

Cited by in corpus (27)

• Quantum cosmology from the de Broglie-Bohm perspective
• Quantum Gravitational Contributions to the CMB Anisotropy Spectrum
• On the quantum fate of singularities in a dark-energy dominated universe
• Quantum cosmology and late-time singularities
• Observations in Quantum Cosmology
• Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity
• Volume average regularization for the Wheeler-DeWitt equation
• Classical and quantum cosmology of the little rip abrupt event
• Can the Arrow of Time be understood from Quantum Cosmology?
• What kind of science is cosmology?
• Quantum mechanics allows setting initial conditions at a cosmological singularity: Gowdy model example
• Baryogenesis in cosmological models with symmetric and asymmetric quantum bounces
• Cosmological models with asymmetric quantum bounces
• Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Making a Quantum Universe: Symmetry and Gravity
• The Functional Schrodinger Equation in the Semiclassical Limit of Quantum Gravity with a Gaussian Clock Field
• Bouncing and inflationary dynamics in quantum cosmology in the de Broglie-Bohm interpretation
• Radiation-dominated bouncing model with slow contraction and inflation
• M-theory Calabi-Yau Quantum Mechanics
• The rotation problem
• Topology and Volume Effects in Quantum Gravity: Wheeler-DeWitt Theory
• Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
• Space, Time, Matter in Quantum Gravity
• Hilbert spaces built over metrics of fixed signature
• An approximate application of quantum gravity to the rotation problem
• Semiclassical Length Measure from a Quantum-Gravity Wave Function