Double expansion in asymptotically free theories

TL;DR

This paper introduces a novel approximation method for asymptotically free theories that combines weak and strong coupling expansions, validated on models with known solutions.

Contribution

It proposes a combined weak-strong coupling expansion scheme for asymptotically free theories, enabling analysis across different energy scales.

Findings

Method successfully tested on low-dimensional models

Intermediate scale where both expansions are valid identified

Provides a new approach to study asymptotically free theories

Abstract

I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy effective theory is solved using the strong coupling expansion. In some models there exists an intermediate scale at which both expansions make sense. The method is tested on few low dimensional models for which an exact solution is known.