Related papers: Quantum geometrodynamics: whence, whither?
Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
The mathematically correct approach to constructing quantum geometrodynamics of a closed universe formulated in Part I is realized on the cosmological Bianchi-IX model with scalar fields. The physical adequacy of the obtained…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting…
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant…
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations. In the second…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never trivial, so that it plays the r\^ole of intrinsic energy. Such a key property selects the Wheeler-DeWitt (WDW) quantum potential…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
In any quantum theory of gravity, it is of the utmost importance to recover the limit of quantum theory in an external spacetime. In quantum geometrodynamics (quantization of general relativity in the Schr\"odinger picture), this leads in…
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the…