SU(N)gauge invariant currents and hadronization

Abstract

The fermion and total currents generated by a gauge field are derived in the framework of a self-consistent consideration of the Dirac and Yang-Mills equations. Under the condition of gauge invariance, the obtained currents are found to be expressible in terms of the massive vector field generated by the initial gauge field. The mass of this vector field depends strongly on the occupancy numbers of the fermion subsystem, whereas the arisen mass term holds the gauge invariance of the modified Lagrangian. We show that such a modified Lagrangian can be reduced to the pure gluodynamic Lagrangian containing a mass term. By breaking the initial $SU(N)$ symmetry, we derive the Lagrangian governing the dynamics of the massive scalar particles, which can be treated as the octet of the pseudoscalar mesons. The contribution of both the quark-gluon interaction and the self-interaction gluon field to the masses of the octet particles is considered. Provided that the hadronization of the confinement matter into the pion triplet occurs, the QCD coupling constant is evaluated in this case in the developed model.