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arXiv · 2207.08555

Perturbation theory for the $Φ^4_3$ measure, revisited with Hopf algebras

Nils Berglund·Tom Klose
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Abstract

We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $Φ^4_3$ 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.

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Nils Berglund, Tom Klose. 2023-10-05. Perturbation theory for the $Φ^4_3$ measure, revisited with Hopf algebras. https://arxiv.org/abs/2207.08555

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