On S-Matrix factorization of the Landau-Lifshitz model

TL;DR

This paper computes the three-particle scattering S-matrix for the Landau-Lifshitz model, demonstrating its factorization at the second order, similar to the non-linear Schrödinger model, thus providing insights into its integrability.

Contribution

It provides the first explicit second-order computation of the three-particle S-matrix for the Landau-Lifshitz model, confirming its factorization property.

Findings

Three-particle S-matrix is factorizable at second order

Methodology parallels that of the non-linear Schrödinger model

Supports integrability of the Landau-Lifshitz model

Abstract

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schr\"{o}dinger model, that the three-particle S-matrix is factorizable in the first non-trivial order.