Comparison of Improved Perturbative Methods

TL;DR

This paper compares two improved perturbative methods, one using a large field cutoff and the other employing a sequence of approximants, analyzing their effectiveness in different coupling regimes for integrals and quantum problems.

Contribution

It provides a comparative analysis of two novel perturbative techniques, highlighting their complementary strengths and potential applications in lattice gauge theory.

Findings

Large field cutoff method excels at strong coupling.

Sequence of approximants performs well at intermediate coupling.

Methods are effective in regimes where traditional series diverge.

Abstract

In many cases of interest, the perturbative series based on conventional Feynman diagrams have a zero radius of convergence. Series with a finite radius of convergence can be obtained by either introducing a large field cutoff or by replacing the exponential of the perturbation by a sequence of approximants as recently proposed by Pollet, Prokof'ev, and Svistunov. We compare these two methods for integrals and quantum mechanical problems. The two methods perform well in complementary regime (strong coupling for the large field cutoff and intermediate coupling for the other method). We briefly discuss potential applications for lattice gauge theory with compact groups (which have a build-in large field cutoff).