Perturbation theory for the $\Phi^4_3$ measure, revisited with Hopf algebras - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

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.

Dates and versions

hal-03726881 , version 1 (19-07-2022)

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