Polynomial Form Factors in the O(3) Nonlinear sigma-Model

TL;DR

This paper investigates the structure of form factors in integrable models, specifically constructing polynomial solutions for key operators in the O(3) sigma-model, enhancing understanding of its mathematical framework.

Contribution

It introduces polynomial solutions for form factors of important operators in the O(3) sigma-model, expanding the analytical tools available for this integrable system.

Findings

Constructed polynomial form factors for spin-field, current, energy-momentum tensor, and topological charge density.

Identified consistency conditions for form factors in integrable models.

Provided new explicit solutions within the O(3) sigma-model framework.

Abstract

We study the general structure of Smirnov's axioms on form factors of local operators in integrable models. We find various consistency conditions that the form factor functions have to satisfy. For the special case of the $O(3)$ $\sigma$-model we construct simple polynomial solutions for the operators of the spin-field, current, energy-momentum tensor and topological charge density.