Related papers: Geometrodynamic Quantization and Time Evolution in…
The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
The higher dimensional Quantum General Relativity of a Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated. The model of quantum geometrodynamics, based on the Wheeler-DeWitt equation…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
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…
The relativistic theory of unconstrained $p$-dimensional membranes ($p$-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…
The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by…
We consider a solution to the problem of time in quantum gravity by deparameterisation of the ADM action in terms of York time, a parameter proportional to the extrinsic curvature of a spatial hypersurface. We study a minisuperspace model…
This work concerns a new reformulation of quantum geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when…
Rovelli's `` quantum mechanics without time'' motivates an intrinsically time-slicing independent picture of reduced phase space quantum gravity, which may be described as ``quantization after evolution''. Sufficient criteria for carrying…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
Conventional approaches to quantum gravity regard quantum principles, such as nonlocality and superposition, as fundamental properties of nature and therefore argue that gravity must also be quantized. In contrast, this work introduces a…
One of the standard approaches of incorporating the quantum gravity (QG) effects into the semiclassical analysis is to adopt the notion of a quantum-corrected spacetime arising from the QG model. This procedure assumes that the expectation…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…