Single-Pole Interaction of the Particle with the String

TL;DR

This paper derives effective equations of motion for a string with particles at its ends, revealing boundary conditions as particle equations of motion and analyzing their properties with a focus on boundary conditions and Regge trajectory corrections.

Contribution

It introduces a generalized Papapetrou method to derive boundary conditions as particle equations of motion for a string with attached particles.

Findings

Boundary conditions correspond to particle equations of motion.

Neumann and Dirichlet boundary conditions are exemplified.

A small correction to Regge trajectories due to particle mass is identified.

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. Various properties of those equations are discussed, and a simple example is treated in detail, exhibiting the properties of Neumann and Dirichlet boundary conditions and giving a small correction term to the law of Regge trajectories due to the nonzero particle mass.