Periodic generalizations of static, self-dual SU(2) gauge fields.

Abstract

Linear pairs are used to inject time dependence (periodic or not) in a particularly simple fashion into static, self-dual SU(2) gauge fields. A canonical formalism is proposed for periodic generalizations of Euclidean versions of monopoles of arbitrary charge. The cases whose static limit corresponds to charges 1 and 2 are studied in some detail. Finite actions over one period are obtained. As nonperiodic examples Witten's solution for arbitrary index is derived in the context of our formalism with one single pole and a class of possible generalizations is indicated. A further generalization of our formalism, in another direction, is sketched. It is based on a coordinate transformation leading to a ``time'' with finite domain. This paper is principally concerned with periodic solutions. Such generalizations of only spherically and axially symmetric static solutions are considered here. The basic formalism, however, is not thus limited.