# Quantum Theory of Gravity. I. The Canonical Theory

@article{Dewitt1967QuantumTO,
title={Quantum Theory of Gravity. I. The Canonical Theory},
author={Bryce S. Dewitt},
journal={Physical Review},
year={1967},
volume={160},
pages={1113-1148}
}
• B. Dewitt
• Published 25 August 1967
• Physics
• Physical Review
Following an historical introduction, the conventional canonical formulation of general relativity theory is presented. The canonical Lagrangian is expressed in terms of the extrinsic and intrinsic curvatures of the hypersurface ${x}^{0}=\mathrm{constant}$, and its relation to the asymptotic field energy in an infinite world is noted. The distinction between finite and infinite worlds is emphasized. In the quantum theory the primary and secondary constraints become conditions on the state…
2,126 Citations

## Figures from this paper

A topological extension of general relativity
A set of algebraic equations for the topological properties of space-time is derived, and used to extend general relativity into the Planck domain. A unique basis set of three-dimensional prime
Quantum geometrodynamics of the Bianchi IX cosmological model
• Physics
• 2006
The canonical quantum theory of gravity?quantum geometrodynamics (QG)?is applied to the homogeneous Bianchi type IX cosmological model. As a result, a framework for the quantum theory of homogeneous
Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry
This thesis concerns with a framework of canonical quantization of gravity based on the EinsteinHilbert action extended by terms quadratic in curvature. The aim is to investigate the semiclassical
Aspects of 3-manifold theory in classical and quantum general relativity
Einstein’s field equation of General Relativity can be cast into the form of evolution equations with well posed Cauchy problem. The object that undergoes evolution is then a Riemannian 3-manifold
OF NONSYMMETRIC GRAVITATIONAL THEORIES
The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as
A Hamiltonian Formulation of Nonsymmetric Gravitational Theories
The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as
Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the Arnowitt-Deser-Misner (ADM) phase space for canonical general relativity to that consisting
Spacelike Singularities and Hidden Symmetries of Gravity
• Physics, Medicine
Living reviews in relativity
• 2008
It is shown that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group.
Symmetry and Evolution in Quantum Gravity
• Physics
• 2014
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of
Loop space representation of quantum general relativity
• Physics
• 1988
Abstract We define a new representation for quantum general relativity, in which exact solutions of the quantum constraints may be obtained. The representation is constructed by means of a