Related papers: Semiclassical states in quantum gravity: Curvature…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We address the "inverse problem" for discrete geometry, which consists in determining whether, given a discrete structure of a type that does not in general imply geometrical information or even a topology, one can associate with it a…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
I describe the first steps in the construction of semiclassical states for non-perturbative canonical quantum gravity using ideas from classical, Riemannian statistical geometry and results from quantum geometry of spin network states. In…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…
We compute the two-point correlation function of the area operator for semiclassical states of loop quantum gravity in the limit of large spins. The cases of intrinsic and extrinsic coherent states are considered, along with a new class of…
We compute numerically the time evolution of simple semiclassical states describing homogeneous and isotropic spatial geometries in quantum-reduced loop gravity under a deparametrized formulation of the dynamics, in which a reference matter…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum…
Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…