An SPDE approach to perturbation theory of $\Phi^4_2$: asymptoticity and short distance behavior

Hao Shen; Rongchan Zhu; Xiangchan Zhu

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arXiv · 2108.11312

An SPDE approach to perturbation theory of $\Phi^4_2$: asymptoticity and short distance behavior

Hao Shen·Rongchan Zhu·Xiangchan Zhu

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Abstract

In this paper we study the perturbation theory of $\Phi^4_2$ 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.

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BibTeX RIS

Hao Shen, Rongchan Zhu, Xiangchan Zhu. 2021-08-25. An SPDE approach to perturbation theory of $\Phi^4_2$: asymptoticity and short distance behavior. https://arxiv.org/abs/2108.11312

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