Related papers: Intersecting Quantum Gravity with Noncommutative G…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
We argue for enlarging the traditional view of quantum gravity, based on "quantizing GR", to include explicitly the non-spatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and…
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 present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and…
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…
Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries,…
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to…
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…
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…
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…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
We study light propagation in the picture of semi-classical space-time that emerges in canonical quantum gravity in the loop representation. In such picture, where space-time exhibits a polymer-like structure at microscales, it is natural…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…