Perturbation theory for the Φ⁴₃ measure, revisited with Hopf algebras

2022/07/18 by Nils Berglund, Tom Klose, Berglund, Nils +1 · 1 citation
Mathematics · Physics and Astronomy · #35R11 (primary) #60H15 #81T17 #82C28 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Probability (math.PR) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2207.08555

openalex publication_date 2022/07/18 · openalex created_date 2022/07/20 · openalex updated_date 2026/07/28

Abstract

We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised Φ⁴₃ 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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