SU(4) and a new class of exact, time-dependent, classical solutions to gauge theories

Abstract

We construct an exact, time-dependent, classical solution to the Yang-Mills equation with SU(4) symmetry, generalizing the static solutions of Wu and Yang. This solution describing a pointlike particle which can execute arbitrary space-time motions is constructed out of Lienard-Wiechert potentials. The solution opens the door to an entirely new class of classical ansatz to gauge theories, including 't Hooft monopoles. Timedependent classical solutions of this type may prove useful in constructing quantized bound-state hadronic systems.