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

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.

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