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

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arxiv 2207.08555 v2 pith:5SJAXC5E submitted 2022-07-18 math-ph math.MPmath.PRquant-ph

Nils Berglund , Tom Klose This is my paper · ORCID
classification math-phmath.MPmath.PRquant-ph
keywords asymptoticmeasureadmitsalgebrasalmostborelboundsbphz
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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 $\Phi^4_3$ 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.

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  1. Renormalising Feynman diagrams with multi-indices

    math-ph 2025-01 conditional novelty 7.0 of 10

    A Hopf algebra on multi-indices with an extraction-contraction coproduct reproduces BPHZ renormalisation and yields the renormalised measure's counterterms directly.

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