Effective dynamics of an electrically charged string with a current

TL;DR

This paper derives and analyzes the effective dynamics of an electrically charged string with current, considering self-action corrections, and explores conditions for stationary states and radiation emission.

Contribution

It introduces a new model for the dynamics of charged strings with current, including self-action effects and constraints from reparametrization invariance.

Findings

Derived equations of motion with self-action corrections.

Identified conditions for stationary states in external electromagnetic fields.

Obtained solutions for charged rings in various field configurations.

Abstract

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparametrization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are revealed. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.