Single-Pole Interaction of the Particle with the String

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.