State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

Geometrical measurements in three-dimensional quantum gravity

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 distances between points, giving spectra and probabilities which have a geometrical interpretation. The observables are related to the evaluation of relativistic spin networks by a Fourier transform.