AN SPDE APPROACH TO PERTURBATION THEORY OF Φ 42: ASYMPTOTICITY AND SHORT DISTANCE BEHAVIOR

In this paper we study the perturbation theory of ?42 model on the whole plane via stochastic quantization. We use integration by parts formula (i.e., Dyson-Schwinger equations) to generate the perturbative expansion for the k-point correlation functions, and prove bounds on the remainder of the trun-cated expansion using PDE estimates; this in particular proves that the ex-pansion is asymptotic. Furthermore, we derive short distance behaviors of the 2-point function and the connected 4-point function, also via suitable Dyson- Schwinger equations combined with PDE arguments.