Perturbation expansions at large order: Results for scalar field theories revisited

TL;DR

This paper revisits the asymptotic behavior of perturbation expansions in scalar field theories, correcting previous errors and providing consistent results for high-order terms, especially in phi^4 theory, with implications for critical exponent calculations.

Contribution

It identifies and corrects errors in earlier high-order behavior results of perturbation expansions, offering a unified and consistent analysis for scalar field theories.

Findings

Corrected high-order behavior results for phi^4 theory

Discussion on renormalization of non-perturbative effects

Insights into Feynman diagrams at large order

Abstract

The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by the differing and incompatible results for the high-order behaviour of the perturbation expansion reported in the literature. We identify the sources of the errors made in earlier papers, correct them, and obtain a consistent set of results. We focus on phi^4 theory, since this has been the most studied and is the most widely used, but we also briefly discuss analogous results for phi^N theory, with N>4. This reexamination of the structure of perturbation expansions raises issues concerning the renormalisation of non-perturbative effects and the nature of the Feynman diagrams at large order, which we discuss.