Strong-Coupling Extrapolation of Gell-Mann--Low Functions

TL;DR

This paper introduces a novel method for extrapolating Gell-Mann-Low functions from weak-coupling expansions to strong-coupling regimes, with applications to quantum field theories.

Contribution

A new extrapolation technique is proposed that accurately extends weak-coupling series to strong coupling, demonstrated on quantum field theory functions.

Findings

Method can reconstruct entire functions from weak-coupling expansions.

Accurate extrapolation of Gell-Mann-Low functions in QED and QCD.

Potential for exact function reconstruction in some cases.

Abstract

Gell-Mann-Low functions can be calculated by means of perturbation theory and expressed as truncated series in powers of asymptotically small coupling parameters. However, it is necessary to know there behavior at finite values of the parameter and, moreover, their behavior at asymptotically large coupling parameters is also important. The problem of extrapolation of weak-coupling expansions to the region of finite and even infinite coupling parameters is considered. A method is suggested allowing for such an extrapolation. The basics of the method are described and illustrations of its applications are given for the examples where its accuracy and convergence can be checked. It is shown that in some cases the method allows for the exact reconstruction of the whole functions from their weak-coupling asymptotic expansions. Gell-Mann-Low functions in multicomponent field theory, quantum electrodynamics, and quantum chromodynamics are extrapolated to their strong-coupling limits.