Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model

TL;DR

This paper compares perturbative and non-perturbative methods in quantum field theory using the O(3) nonlinear sigma model, showing that form factor techniques are highly accurate below certain energies and perturbation theory becomes valid only at higher energies.

Contribution

It demonstrates that the form factor approach, truncated at six particles, effectively solves the model in a broad energy range, clarifying the transition to perturbative behavior.

Findings

Form factor approach is nearly exact below 10^4 m.

Perturbative regime begins around 100 m.

Two-point functions reveal energy-dependent regimes.

Abstract

The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 10^4 in units of the mass gap $m$. We argue that the form factor approach, with the form factor series trunctated at the 6-particle level, provides an almost exact solution of the model in this energy range. The onset of the (2-loop) perturbative regime is found to occur only at energies around $100m$.