Related papers: A New Approach in Quantum Gravity and its Cosmolog…
We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical…
We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by…
The quantum theory of the spherically symmetric gravity in 3+1 dimensions is investigated. The functional measures are explicitly evaluated and the physical state conditions are derived by using the technique developed in two dimensional…
This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
We use a quantum mechanical charged particle as a test particle which probes the dynamics of force-related fields it is subject to. We allow for geodesic motion and relations involving gravitation appear. Gravitation affects quantum…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We explore the symmetry reduced form of a non-perturbative solution to the constraints of quantum gravity corresponding to quantum de Sitter space. The system has a remarkably precise analogy with the non-relativistic formulation of a…
Using the ADM formalism, we demonstrate that the Hamiltonian formulation of Quantum Gravity is exactly in the form of a worldline (WL) formalism in the superspace. We then show that the Keldysh partition function reduces to the partition…
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…
The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which…
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…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…
In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant {\Lambda} and try to make contact with alternative quantization approaches already…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
We discuss predictions for cosmology which result from the scaling solution of functional flow equations for a quantum field theory of gravity. A scaling solution is necessary to render quantum gravity renormalizable. Our scaling solution…