Nonperturbative Lorentzian path integral for gravity

We construct a well-defined regularized path integral for Lorentzian quantu m gravity in terms of dynamically triangulated causal space-times. Each Lor entzian geometry and its action have a unique Wick rotation to the Euclidea n sector. All space-time histories possess a distinguished notion of a disc rete proper time and, for finite lattice volume, the associated transfer ma trix is self-adjoint, bounded. and strictly positive. The degenerate geomet ric phases found in dynamically triangulated Euclidean gravity are not pres ent.