Related papers: Exact uncertainty principle and quantization: impl…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically…
The basic features of a quantum field theory which is Poincar\'e invariant, gauge invariant, finite and unitary to all orders of perturbation theory are reviewed. Quantum gravity is finite and unitary to all orders of perturbation theory.…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
A variational framework for the quantization of gravitational fields is developed based on an extension of the stationary action principle. Within this framework, the Wheeler-DeWitt equation for the gravitational wave functional is…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation,…
We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
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…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
One of the leading issues in quantum field theory and cosmology is the mismatch between the observed and calculated values for the cosmological constant in Einstein's field equations of up to 120 orders of magnitude. In this paper, we…