Merons and meronlike configurations

Abstract

We study successively for SU(2), SU(3), and SU(4) gauge groups and for Euclidean metric singular solutions of the equations of motions for "meronlike" Ans\"atze, namely for ${A}_{\ensuremath{\mu}}=(\frac{1}{2})i({\ensuremath{\partial}}_{\ensuremath{\mu}}U){U}^{\ensuremath{-}1}$, where $U$ is chosen among particular classes of gauge operators for the groups in question. For SU(3) and SU(4), apart from generalizations of logarithmically divergent SU(2) solutions, we construct explicity new classes of solutions which have meron-type topological index but a stronger than logarithmic divergence in the action. The study of a possible hierarchy of divergent solutions is thus initiated. But we start with a brief recapitulation of known SU(2) solutions mostly in order to study, carefully and in detail, the consequences of certain classes of singular gauge transformations. We show very explicitly that using them, solutions with a continuous spectrum of the topological index are obtained. Implications of our results are discussed.