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

• 成果类型: Article
• 署名作者: Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1873
• 发表日期: 2023
• 页码: 2600-2642
• 关键词: random-walk representation; classical spin systems; stochastic quantization; paracontrolled distributions; wightman axioms; field; MODEL; inequalities; expansion; limit

摘要

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.