Self-similar extrapolation in quantum field theory

TL;DR

This paper introduces a self-similar approximation method to extrapolate divergent asymptotic series in quantum field theory, enabling calculations at finite and infinite coupling parameters.

Contribution

It presents a novel self-similar factor approximation technique that extends the applicability of perturbation series beyond their usual convergence limits.

Findings

Effective extrapolation of asymptotic series demonstrated

Method applicable to rational, irrational, and transcendental functions

Improved calculations in quantum field theory problems

Abstract

Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a rule are divergent for finite values of the parameters. In this paper, a method is described allowing for the extrapolation of such asymptotic series to finite values of the coupling parameters, and even to their infinite limits. The method is based on self-similar approximation theory. This theory approximates well a large class of functions, rational, irrational, and transcendental. A method is presented, resulting in self-similar factor approximants allowing for the extrapolation of functions to arbitrary values of coupling parameters from only the knowledge of expansions in powers of small coupling parameters. The efficiency of the method is illustrated by several problems of quantum field theory.