Additive structure of a hierarchy of self-dual SU(2) gauge fields

Abstract

Four dimensional, self-dual SU(2) gauge fields depending, in a properly chosen gauge, on only two coordinates are considered. Finite domains of the other two coordinates make possible finite actions over the entire space-time. Harrison-Neugebauer-type transformations are displayed in a particularly simple additive form. Just by adding logarithmic derivatives of certain functions to the gauge potentials one passes from one Atiyah-Ward class to another. Restrictions on the metric necessary for the formalism to work are derived. Singularities are not excluded from the outset. This allows a unified treatment of various cases including that of an accelerated observer and of one straight cosmic string. Only the essential structure is briefly presented.