Towards a String Formulation of Vortex Dynamics

TL;DR

This paper derives an exact equation of motion for vortices in complex field models, exploring how to reduce field dynamics to a string-based dynamical system with non-local interactions.

Contribution

It introduces a precise vortex motion equation and discusses the reduction of field dynamics to a string-based model with non-local interactions.

Findings

Derived an exact vortex motion equation

Analyzed reduction of field dynamics to string models

Discussed non-local interactions in vortex systems

Abstract

We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom.