Soliton form factors from lattice simulations

TL;DR

This paper demonstrates a numerical lattice Monte Carlo method to compute soliton form factors in quantum theories, validated by matching results with the exactly known Ising model near criticality.

Contribution

It introduces a general lattice simulation approach for calculating soliton form factors, applicable across various models and validated against known results.

Findings

Form factors can be accurately computed using lattice Monte Carlo simulations.

The method's results agree with the exact Ising model form factor near the critical point.

The approach is versatile and applicable to different types of solitons.

Abstract

The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in 1+1-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model.