The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third quantization of two-dimensional surfaces based on the method of causal dynamical triangulation (CDT). Formally, our construction is similar to the c = 0 non-critical string field theory developed by Ishibashi, Kawai and others, but physically it is quite dist...