Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

TL;DR

This paper introduces simplified nonlinear integral equations for calculating finite volume excited state energies in O(3) and O(4) nonlinear sigma-models, making numerical analysis more feasible and confirming accuracy with existing TBA results.

Contribution

It presents a new finite component nonlinear integral equation approach that simplifies numerical computation of excited states in these models.

Findings

Numerical results agree with previous TBA calculations within precision.

The new equations are easier to solve numerically due to finite components.

The approach improves computational efficiency for excited state energies.

Abstract

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.