Electromagnetic self interaction in strings

TL;DR

This paper develops a relativistic framework for modeling electromagnetic self-interactions in string models, using a covariant Green measure and regularized gradient operator to handle the effects at leading order.

Contribution

It introduces a covariant string-source Green measure and a regularized gradient operator to describe electromagnetic self-interactions in a general class of string models.

Findings

Provides a coherent relativistic scheme for electromagnetic self-interaction.

Employs a regularized gradient operator incorporating extrinsic curvature.

Applicable to a broad range of string models at leading order.

Abstract

To facilitate the treatment of electromagnetic effects in applications such as dynamically perturbed vortons, this work employs a covariantly formulated string-source Green measure to obtain a coherent relativistic scheme for describing the self interaction of electromagnetic currents in string models of a very general kind, at leading order in the relevant field gradients, using a regularised gradient operator given by $\hat\nabla_\nu=$ $\bar\nabla_\nu +{1\over 2} K_\nu$ where $\bar\nabla_\nu$ is the usual tangential gradient operator and $K_\nu$ is the extrinsic curvature vector.