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

Abstract

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

26 pages. Extended discussion of literature and modified statements w.r.t. Borel resummation

References in corpus (1)

• Hopf-algebraic deformations of products and Wick polynomials