Some Exact Multipseudoparticle Solutions of Classical Yang-Mills Theory

Abstract

I present some exact solutions of the Polyakov-Belavin-Schwartz-Tyupkin equation $F_{\mu \nu }={\tilde{F}}_{\mu \nu }$ for an SU(2) gauge theory in Euclidean space. My solutions describe a system with an arbitrary number of pseudoparticles, with arbitrary scale parameters and arbitrary separations, arranged along a line. The action for an $n$-pseudoparticle solution is precisely $n$ times the action for a single pseudoparticle.