Effective Lagrangian and equations for valence quark and gluon Green's functions

Abstract

Starting from the QCD Lagrangian and separating background and valence degrees of freedom, one arrives at the effective Lagrangian for valence quarks and gluons. Each term in the Lagrangian contains a product of valence quark and gluon operators acting at the end of the fundamental or adjoint string, made of the background field. A simple procedure is described how to obtain from the Lagrangian self-coupled equations for quark and gluon Green's function.