Dynamical regimes of the QCD string with quarks

This a short report on the first paper (A. Dubin, A. Kaidalov and Yu. Simonov:Yad. Fiz.,56, No. 12 (1993)) of a series devoted to quantum dynamics of the quark-antiquark system at large distances. Starting from the QCD Lagrangian, we derive the effective action for a massive quark and antiquark at large distances, corresponding to the minimal-area law of the Wilson loop. The path integral method is used to quantize the system and the spectrum is obtained with asymptotically linear Regge trajectories. Two dynamical regimes distinguished by the string energy-momentum distribution are found: at large orbital excitations (l≫1) the system behaves as a string and yields the Regge slope of 1/2πσ, while at smalll one obtains a potential-like regime for the relativistic or non-relativistic system. The problem of relative time is clarified. It is shown that in the valence-quark approximation one can reduce the initial four-dimensional dynamics to three dimensions.