Vacuum polarization and the absence of free quarks in four dimensions

Abstract

We speculate that the mechanism of one-dimensional quantum electrodynamics for prohibiting quark production can be generalized to three-dimensional space. The important feature of one-dimensional gauge theories which trap quarks is that electric flux lines cannot spread out and can only end on a charge. The generalization to three dimensions involves dynamical nonlinearities which trap electric flux lines into tubelike configurations. It is suggested that the required nonlinearities arise in Yang-Mills theories of "colored" quarks. The large-scale properties of hadrons would be described by a stringlike model similar to the conventional dual model.