Large Field Cutoffs Make Perturbative Series Converge

TL;DR

This paper demonstrates that applying large field cutoffs in lambda phi^4 theories yields convergent perturbative series that approximate exact results more effectively than traditional summation methods, especially for larger coupling constants.

Contribution

It introduces a method of using large field cutoffs to achieve convergent perturbative series in lambda phi^4 problems, outperforming Pade and Borel summations for certain couplings.

Findings

Modified series converge exponentially close to exact values

Method outperforms Pade and Borel summations for large lambda

Effective even when Borel sum has singularities

Abstract

For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade approximants and Borel summations. We discuss some aspects of the semi-classical methods used to calculate the modified Feynman rules and estimate the error associated with the procedure. We provide a simple numerical example where the procedure works despite the fact that the Borel sum has singularities on the positive real axis.