The Confinement Mechanism in Yang-Mills Theory?

Abstract

Using the recently proposed non-linear gauge condition, we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the non-linear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The non-linear sector is actually composed of "Gribov horizons" on the surfaces parallel to the Coulomb surface. In this sector, the gauge field can be expressed in terms of a scalar field and a new vector field. The effective dynamics of the scalar field suggests non-perturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) scalar fields are classical solutions and averaging these solutions using a qaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of the surfaces parallel to the Coulomb surface.