THE STRUCTURE OF PRINCIPAL BUNDLES FOR DUAL CHARGES IN GAUGE THEORIES

<正> In the gauge theory for electromagnetism, the properties of electromagnetic fields around a magnetic monopole g （the dual charge of electric charges） can be described in terms of the nontrivial principal U1-bundle PD （S2, U1） over S2 （D=2eg being an integer）. In this paper, we discuss the topological properties of nontrivial U1-bundles and their metric structure as Riemann manifolds. It is shown that PD（S2, U1） is isomorphic to the Hopf bundle S3/ZD, and that, for a static monopole, defining the metric properly makes PD （S2, U1） itself S3/ZDFurthermore, with SU2 gauge fields as example, we examine the problem of how to introduce the concept of the dual charge into non-Abelian gauge theories, and discuss the topological classification of corresponding principal bundles. On the basis of homotopic classification theory of bundles over spheres, it is pointed out that the equivalence classes （i. c., the gauge types） of SU2 gauge fields on S4≈ can be characterized by the dual charges corre