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

Abstract

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

37 pages. Small fixes in Appendix A

References in corpus (2)

• Large $N$ limit of the $O(N)$ linear sigma model in 3D
• The ${\Phi }_3^4$ measure has sub-Gaussian tails

Cited by in corpus (3)

• Large $N$ limit of the $O(N)$ linear sigma model in 3D
• A stochastic PDE approach to large N problems in quantum field theory: a survey
• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization