Magnetic charge of finite lifetime in SU(2) gluodynamics

Abstract

A self-dual, localized solution to the classical SU(2) Yang-Mills equation in Euclidean spacetime, which formally possesses infinite action, is investigated in view of its U(1) charge content after Abelian projection. This is suggested by noting that the solution satisfies 't Hooft's differential projection condition away from the singularities. As a result the existence of dynamical, magnetic charge of finite lifetime is established. A covariant cutoff for the action is introduced by demanding the solution to be close to an instanton topologically. This is in analogy to the \underline{calculation} of the mass of a point charge in classical electrodynamics or the subtraction of diverging self-energies of magnetic monopoles as discussed in the literature. The Wilson loop is evaluated in the background of a dilute gas. Assuming identical integrals over size distributions, the corresponding static quark/anti-quark potential at infinite spatial separation can be seizably higher than the potential in a dilute instanton gas.