Interaction of the Particle with the String in Pole-Dipole Approximation

TL;DR

This paper derives equations of motion for a string with particles at its ends, revealing boundary conditions as particle equations and analyzing corrections to Regge trajectories due to particle angular momenta.

Contribution

It introduces a generalized approach to model a string with particles at its ends, deriving boundary conditions as particle equations of motion and analyzing their effects on Regge trajectories.

Findings

Derived effective equations of motion for the string-particle system.

Solved boundary conditions explicitly for a rotating straight string.

Identified correction terms to Regge trajectories from particle angular momenta.

Abstract

Within the framework of generalized Papapetrou method, we derive the effective equations of motion for a string with two particles attached to its ends, along with appropriate boundary conditions. The equations of motion are the usual Nambu-Goto-like equations, while boundary conditions turn out to be equations of motion for the particles at the string ends. The form of those equations is discussed, and they are explicitly solved for a particular case of a straight-line string rotating around its center. From this solution we obtain the correction terms to the $J\propto E^2$ law describing Regge trajectories, due to nonzero angular momenta of the particles.