Non-perturbative Lorentzian quantum gravity, causality and topology change

We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a cau sal structure. The model can be solved exactly at the discretized level. It s continuum limit coincides with the theory obtained by quantizing 2d conti nuum gravity in proper-time gauge, but it disagrees with 2d gravity defined via matrix models or Liouville theory. By allowing topology change of the compact spatial slices (i.e. baby universe creation), one obtains agreement with the matrix models and Liouville theory. (C) 1999 Elsevier Science B.V .