Related papers: Simplicial Quantum Gravity and Random Lattices
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
The central topic of this thesis is two dimensional Quantum Gravity and its properties. The term Quantum Gravity itself is ambiguous as there are many proposals for its correct formulation and none of them have been verified experimentally.…
The Regge Calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge Model…
We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum…
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its…
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show…
We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…
A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our…
We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a…
Causal dynamical triangulations (CDT) can be used as a regularization of quantum gravity. In two dimensions the theory can be solved anlytically, even before the cut-off is removed and one can study in detail how to take the continuum…
We study 2D quantum gravity on spherical topologies using the Regge calculus approach. Our goal is to shed new light upon the validity of the Regge approach to quantum gravity, which has recently been questioned in the literature. We…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
Contents: 1. Introduction 2. Bosonic propagators and random paths 3. Random surfaces and strings 4. Matrix models and two-dimensional quantum gravity 5. The mystery of $c > 1$ 6. Euclidean quantum gravity in $d > 2$ 7. Discussion
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…
Recent models for discrete euclidean quantum gravity incorporate a sum over simplicial triangulations. We describe an algorithm for simulating such models in general dimensions. As illustration we show results from simulations in four…
I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
We study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are…