Collective model of the hadrons

We describe a model of the baryons and mesons as trilocal and bilocal collective excitations of a self-consistent ground state. The fundamental theory we adopt (in analogy with the BCS Hamiltonian) is quantum chromodynamics (QCD). The hadrons are flavored excitations of a color-singlet vacuum condensate of $\overline{q}q$ pairs. Our approach is completely conventional, fully relativistic, and incorporates both a ${\gamma }_5$-noninvariant vacuum [partially conserved axial-vector current (PCAC)] and quark confinement. We derive the Gor'kov or gap excitation equations for mesons from QCD. These Gor'kov equations provide the connection between QCD and the phenomenological theory of the hadrons. We also discuss the solutions to the gap equation and the gap excitation equation for confined quarks. It is noted that for an infrared-singular gauge field propagator the exact gap equation becomes a differential equation for the quark propagator. These equations are solved analytically and have the property of PCAC and confinement in the infrared limit. Qualitatively, the same features are found as in two-dimensional QCD. The Gor'kov equations for the bound states are obtained, and the ground-state meson mass spectrum is computed. Potentially, this approach can provide for the determination of the fundamental features of hadron phenomenology.