Classical Euclidean field configurations and charge confinement

Abstract

The possibility of the confinement of external charge in a pure Yang-Mills theory is discussed. Only field configurations which almost obey the classical field equations are considered. The two- and three-dimensional models of Callan, Dashen, and Gross and of Polyakov are reviewed. If confinement occurs in a four-dimensional pure Yang-Mills theory it is concluded that field configurations which are far from obeying the Euclidean classical equations of motion must be predominant.