Related papers: Applications of Random Graphs to 2D Quantum Gravit…
We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we…
We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three…
We study the implications of the simplicity constraint in the spincube model of quantum gravity. By relating the edge-lengths to the integer areas of triangles, the simplicity constraint imposes very strong restrictions between them,…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
In this article we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated and their relationship with the…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. We show that there exists an effective transfer matrix labeled by the scale factor which properly describes the evolution of the quantum universe. In…
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet…
We review a recently introduced effective graph approximation of causal dynamical triangulations (CDT), the multigraph ensemble. We argue that it is well suited for analytical computations and that it captures the physical degrees of…
To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…
This is my PhD thesis on four-dimensional simplicial quantum gravity using the dynamical triangulation model. Most of the results we have published in separate papers are collected here for your convenience. Some new results have been added…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we…
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…
This Ph.D. thesis pursues two goals: The study of the geometrical structure of two-dimensional quantum gravity and in particular its fractal nature. To address these questions we review the continuum formalism of quantum gravity with…
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…
Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining…
Recently an alternate technique for numerical quantum gravity, dynamical triangulation, has been developed. In this method, the geometry is varied by adding and subtracting equilateral simplices from the simplicial complex. This method…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…