Related papers: On the exponential bound in four dimensional simpl…
We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical…
A crucial requirement for the standard interpretation of Monte Carlo simulations of simplicial quantum gravity is the existence of an exponential bound that makes the partition function well-defined. We present numerical data favoring the…
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.…
Simplicial approximation and the ideas associated with the Regge calculus.provide a concrete way of implementing a sum over histories formulation ofquantum gravity. A four-dimensional simplicial geometry is made up of flat four-simplices…
It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and…
We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set…
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…
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…
We extend simulations of simplicial gravity in four dimensions to include {\it degenerate} triangulations and demonstrate that using this ensemble the geometric finite-size effects are much reduced. We provide strong numerical evidence for…
Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations…
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…
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…
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…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
In the weak-coupling limit, kappa_0 going to infinity, the partition function of simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
We study 4d simplicial quantum gravity in the dynamical triangulation approach with a non-trivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the…
Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although…