Confinement, Nonlocal Field Theory, and Electromagnetic Interation

Abstract

Confinement is usually thought to evolve as a property of the exact solution of a field theory; it does not exist to any finite order of perturbation theory. Recently, an interesting alternative possibility to describe confinement has been suggested by Dubnickova and Efimov [1]. These authors introduce a Lagrangian for the free quark field (called virton field in this context) such that the field operator itself comes out identically zero, the causal propagator, however, is nonzero. A theory like this cannot be formulated in local Lagrangian field theory, but is shown to be possible in the framework of nonlocal Lagrangians. It is now tempting to introduce an interaction for the virtons such that simple perturbation theory in the interaction picture can be applied. Since there are no one virton states, virton-virton scattering amplitudes must vanish identically to any finite order of perturbation theory. Nontrivial results for hadron scattering are only obtained by solving a nonperturbative bound state problem. Hence perturbation theory is not useful if only strong interactions are present. In this note, we introduce an electromagnetic coupling of the virtons to the photon field.