Mathematical Physics
[Submitted on 18 Jul 2022 (v1), last revised 5 Oct 2023 (this version, v2)]
Title:Perturbation theory for the $Φ^4_3$ measure, revisited with Hopf algebras
View PDFAbstract: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.
Submission history
From: Nils Berglund [view email][v1] Mon, 18 Jul 2022 12:22:10 UTC (49 KB)
[v2] Thu, 5 Oct 2023 20:34:29 UTC (70 KB)
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