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

Shen H, Zhu R, Zhu X (2021)
arXiv:2108.11312.

Preprint | Englisch

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Abstract / Bemerkung
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.
Erscheinungsjahr
2021
Zeitschriftentitel
arXiv:2108.11312
Page URI
https://pub.uni-bielefeld.de/record/2958510

### Zitieren

Shen H, Zhu R, Zhu X. An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior. arXiv:2108.11312. 2021.
Shen, H., Zhu, R., & Zhu, X. (2021). An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior. arXiv:2108.11312
Shen, H., Zhu, R., and Zhu, X. (2021). An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior. arXiv:2108.11312.
Shen, H., Zhu, R., & Zhu, X., 2021. An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior. arXiv:2108.11312.
H. Shen, R. Zhu, and X. Zhu, “An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior”, arXiv:2108.11312, 2021.
Shen, H., Zhu, R., Zhu, X.: An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior. arXiv:2108.11312. (2021).
Shen, Hao, Zhu, Rongchan, and Zhu, Xiangchan. “An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior”. arXiv:2108.11312 (2021).

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### Quellen

arXiv: 2108.11312

Inspire: 1912264