Related papers: Numerical quantum gravity by dynamical triangulati…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic…
We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess…
We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show…
We consider the four-dimensional Euclidean dynamical triangulations lattice model of quantum gravity based on triangulations of $S^{4}$. We couple it minimally to a scalar field in the quenched approximation. Our results suggest a…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
Starting from the canonical phase space for discretised (4d) BF-theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection…
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 seeking to arrive at a theory of ``quantum gravity'', one faces several choices among alternative approaches. I list some of these ``forks in the road'' and offer reasons for taking one alternative over the other. In particular, I…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
A nonrelativistic approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach can be used to point out problems and prospects inherent in a more exact theory of quantum…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed…
We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows…
Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the CDT results were obtained for the spatial…
"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be…
The application of quantum theory to gravity is beset with many technical and conceptual problems. After a short tour d'horizon of recent attempts to master those problems by the introduction of new approaches, we show that the aim, a…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…