AN SPDE APPROACH TO PERTURBATION THEORY OF Φ⁴₂: ASYMPTOTICITY AND SHORT DISTANCE BEHAVIOR

In this paper we study the perturbation theory of Φ⁴₂ 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 truncated expansion using PDE estimates; this in particular proves that the expansion 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.