Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated in a background-independent way. After summarizing the status quo of discrete covariant lattice mod...

We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a “Hamiltonian formalism” in which the geodesic distance plays the role of time. Applying this formalism, we obtain a universal function which describes the fractal structures of two dimensional quantum gravity in the continuum limit. Recent developments of two-dimensional gravity h...

In Einstein’s gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equallyspaced spectrum for large quantum numbers. But in more general theories (like, for example, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is n...

There are two related schools attempting at a lattice theory of quantum gravity, dynamical triangulation and Regge quantum gravity. We concentrate on the latter approach and refer to [1,2] for excellent reviews of the former framework. In particular we investigate different formulations, all of them based on the original work by Regge [3], namely conventional Regge gravity [4,5], a group theore...