Coupling Constants in Asymptotic Expansions

TL;DR

This paper introduces a perturbation group approach to address the limitations of traditional perturbation theory, demonstrating that the coupling constant diminishes at high perturbation orders, aligning with Dyson's expectations.

Contribution

It proposes a novel perturbation group framework that extends the applicability of perturbation theory to finite perturbations and analyzes the behavior of coupling constants.

Findings

Coupling constant approaches zero at high perturbation orders

Perturbation group method extends traditional perturbation theory

Aligns with Dyson's hypothesis on perturbation behavior

Abstract

Perturbation theory is a powerful tool in manipulating dynamical system. However, it is legal only for infinitesimal perturbations. We propose to dispose this problem by means of perturbation group, and find that the coupling constant approaches to zero in the limit of high order perturbations as Dyson once expected.