Nonperturbative lorentzian path integral for gravity
We construct a well-defined regularized path integral for Lorentzian quantum gravity in terms of dynamically triangulated causal space-times. Each Lorentzian geometry and its action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time and, for finite lattice volume, the associated transfer matrix is self-adjoint, bounded, and strictly positive. The degenerate geometric phases found in dynamically triangulated Euclidean gravity are not present.
Ambjorn
J
The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.
Jurkiewicz
J
Loll
R