THE CLASSICAL RELATIVISTIC QUARK MODEL IN THE REST FRAME WIGNER – COVARIANT COULOMB GAUGE

Abstract

The system of N scalar particles with Grassman-valued color changes plus the color SU(3) Yang–Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the Wigner-covariant rest frame instant form of dynamics (covariant Coulomb gauge) is given. From the reduced Hamilton equations we extract the second order equations of motion for both the reduced transverse color field and the particles. Then we study this relativistic scalar quark model, deduced from the classical QCD Lagrangian and with the color field present, in the N=2 (meson) case. A special form of the requirement of having only color singlets, suited for a field-independent quark model, produces a "pseudoclassical asymptotic freedom" and a regularization of the quark self-energy.