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) gauge potential on the sphere bundle of a compact and oriented four-dimensional manifold is given. Using this decomposition theory the SU(2) Chern density has been studied in detail. It shows that the SU(2) Chern 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 essential to the topological properties of a manifold. It is shown that there exists the crucial case of branch process at the zero points. Based on the implicit function theorem and the Taylor expansion, the bifurcation of the Chern density is detailed in the neighborhoods of the bifurcation points of phi. It is pointed out that, since the Chern density is a topological invariant, the sum topological chargers of the branches will remain constant during the bifurcation process. (C) 1998 American Institute of Physics.