Pseudoparticle parameters for arbitrary gauge groups

Abstract

The number of parameters entering a Euclidean Yang-Mills solution with topological charge $k$ is determined for a theory constructed from an arbitrary Lie group $G$. It is shown that this number is precisely that required to specify the position, scale, and relative group orientation of $k$ independent solutions each with minimum topological charge 1. Such minimal single-pseudoparticle solutions can be obtained by embedding the familiar ${\mathrm{SU}}_2$ pseudoparticle of Belavin et al. into the general Lie group.