THE GENERAL DECOMPOSITION-THEORY OF SU(2) GAUGE POTENTIAL, TOPOLOGICAL-STRUCTURE AND BIFURCATION OF SU(2) CHERN DENSITY

By means of the geometric algebra the general decomposition of SU(2) g auge potential on the sphere bundle of a compact and oriented four-dim ensional manifold is given. Using this decomposition theory the SU(2) Chern density has been studied in detail. It shows that the SU(2) Cher n density can be expressed in terms of the delta-function delta(phi). One can also find that the zero points of the vector fields phi are es sential to the topological properties of a manifold. It is shown that there exists the crucial case of branch process at the zero points. Ba sed on the implicit function theorem and the Taylor expansion, the bif urcation of the Chern density is detailed in the neighborhoods of the bifurcation points of phi. It is pointed out that, since the Chern den sity is a topological invariant, the sum topological chargers of the b ranches will remain constant during the bifurcation process. (C) 1998 American Institute of Physics.