Perturbation theory for the Φ⁴₃ measure, revisited with Hopf algebras

Nils Berglund and Tom Klose
(2022)

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.

Mathematical Subject Classification: 60H15, 35R11 (primary), 81T17, 82C28 (secondary).

Keywords and phrases: Phi-four-three model, BPHZ renormalisation, Hopf algebras, Wiener chaos expansion, cumulants.

 

PDF file (248 Kb) hal-03726881 arXiv/2207.08555