Related papers: Quantum geometrodynamics: whence, whither?
We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a non-classical geometrodynamics (in the ADM formalism)…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
A possible solution of the problem of time in the Wheeler - DeWitt quantum geometrodynamics is that time appears in semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the…
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation…
The Wheeler - DeWitt geometrodynamics, as the first attempt to develop a quantum theory of gravity, faces certain challenges, including the problem of time and the interpretation of the wave function. In this paper, we present the extended…
The Wheeler -- DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature the opinion that the Wheeler -- DeWitt equation is even more…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the…
The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…