Discrete Lorentzian Quantum Gravity

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 models for four-dimensional quantum gravity, I describe a new class of discrete gravity models whose starting point is a path integral over Lorentzian (rather than Euclidean) space-time geometries. A number of interesting and unexpected results that have been obtained for these dynamically triangulated models in two and three dimensions make discrete Lorentzian gravity a promising candidate for a non-trivial theory of quantum gravity