Causal random geometry from stochastic quantization

Abstract

In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries.

5 pages, 2 figures, presented at XI Latin American Workshop on Nonlinear Phenomena, Buzios, 2009, accepted for publication in Journal of Physics: Conference Proceedings