Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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30 pages, 5 figures, Latex, uses psfig.sty

Scientific paper

10.1016/S0550-3213(98)00692-0

We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d continuum 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.

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