Applications of Hyper-Complex Analysis in Yang-Mills Gauge Theories.

In this paper we show how hyper-complex analysis can be used to explicitly construct self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We shall use a hyper-complex argument principle to establish a natural link between the fundamental solutions of DΔf = 0 and the second Chern class of the SU(2) principal bundles over these manifolds. The considered base manifolds of the bundles are not simply-connected, in general. Actually, the paper summarizes an extension of the corresponding results of Gürsey and Tze on a hyper-complex analytical description of SU(2) instantons. [ABSTRACT FROM AUTHOR]