  We discuss uniform infinite causal triangulations and equivalence to the size
biased branching process measure - the critical Galton-Watson branching process
distribution conditioned on non-extinction. Using known results from the theory
of branching processes, this relation is used to prove weak convergence of the
joint length-area process of a uniform infinite causal triangulations to a
limiting diffusion. The diffusion equation enables us to determine the physical
Hamiltonian and Green's function from the Feynman-Kac procedure, providing us
with a mathematical rigorous proof of certain scaling limits of causal
dynamical triangulations.
