Harrison-Neugebauer-type transformations for instantons: Multicharged monopoles as limits

Abstract

A new formulation, leading to agreeable simplifications, is given, in Sec. II, for constructing axially symmetric, multicharged monopoles through nonlinear superpositions. The ansatz introduced for this end is related to a modification of Yang's $R$ gauge, which we call the "spherical" $R$ gauge. This aspect of Sec. II is taken up in the Appendix. In Sec. III, we generalize our formalism to give a parallel construction for a particular hierarchy of instanton configurations which have the above-mentioned monopoles as static limits obtained through rescaling. Harrison-Neugebauer-type transformations are adapted to the case of finite action through a technique (conveniently termed the "de Sitter trick," though we are concerned here with flat Euclidean space) found useful previously. This is recapitulated in Sec. III. The action and a crucial regularity constraint are studied in Sec. IV. Possible further developments are indicated in the concluding remarks.