Related papers: Smooth quantum gravity: Exotic smoothness and Quan…
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 previous work, we proposed a general framework of positive topological field theories (TFTs) based on Eilenberg's notion of summation completeness for semirings. In the present paper, we apply this framework in constructing explicitly a…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
For more than 80 years theoretical physicists have been trying to develop a theory of quantum gravity which would successfully combine the tenets of Einstein's theory of general relativity (GR) together with those of quantum field theory.…
We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
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 argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
Many approaches to quantum gravity require replacing the traditional black hole geometry with an Exotic Compact Object (ECO), which has a large but not infinite redshift at its surface. We argue that near the ECO surface, the vacuum…
We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability)…
Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…