Non-Perturbative Approach to the Long Distance Behavior of Yang-Mills Theory and the Problem of Quark Confinement in QCD

Abstract

Quantum chromodynamics (QCD), the theory of interacting quarks and gluons, is a natural generalization of quantum electrodynamics (QED), the theory of interacting electrons and photons. In QCD the gauge symmetry of QED is generalized to a non Abelian SU(3) local symmetry in which the vector fields transform like the octet (adjoint) representation of SU(3) and hence carry the charge (color) associated with symmetry. This means that the gluons contribute to the vacuum polarization of the color charge which determines the forces and energies in QCD. All known hadrons are color singlets, i.e., their wave functions are invariant under SU(3) color rotations. This phenomenon, called color confinement, could be explained if the solution of the equations of QCD yield long range forces which impede the separation of color charge or equivalently give infinite energy to an isolated state of non-zero color.