A constituent quark-antiquark effective Lagrangian based on the dual superconducting model of long distance QCD

We review the assumptions leading to the description of long distance QCD by a Lagrangian density expressed in terms of dual potentials. We find the color field distribution surrounding a quark-antiquark pair to first order in their velocities. Using this distribution we eliminate the dual potentials from the Lagrangian density and obtain an effective interaction Lagrangian L(l)(x(1),x(2);v(1),v(2)) depending only upon the quark and antiquark coordinates and velocities, valid to second order in their velocities. We propose LI as the Lagrangian describing the long distance interaction between constituent quarks. In this paper, for simplicity of presentation, we treat the quarks as classical particles.