Quantization of almost-circular orbits in the Fokker action formalism. Regge trajectories

Abstract: A relativistic quark model of mesons formulated within the formalism of Fokker-type action integrals is proposed, in which an interquark interaction is mediated by scalar-vector superposition of higher derivative fields. In the non-relativistic limit the model describes a two-particle system with the linear potential. In order to analyze the model in the essentially relativistic domain the perturbed circular orbit approximation and certain principle of selection of physically meaningful solutions are applied which permit one to perform the canonical quantization of the model. It is shown that the model reproduces well specific features of the light meson spectroscopy.