# Perturbation theory for the $\Phi^4_3$ measure, revisited with Hopf algebras

Abstract : We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $\Phi^4_3$ measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We also examine the question of Borel summability of the asymptotic series. The proofs are based on Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03726881
Contributor : Nils Berglund Connect in order to contact the contributor
Submitted on : Tuesday, July 19, 2022 - 6:55:30 AM
Last modification on : Wednesday, July 20, 2022 - 3:32:01 AM

### Identifiers

• HAL Id : hal-03726881, version 1
• ARXIV : 2207.08555

### Citation

Nils Berglund, Tom Klose. Perturbation theory for the $\Phi^4_3$ measure, revisited with Hopf algebras. 2022. ⟨hal-03726881⟩

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