Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-08
J.Math.Phys. 39 (1998) 4343-4355
Physics
High Energy Physics
High Energy Physics - Theory
revtex, 21pages, no figure
Scientific paper
10.1063/1.532515
By means of the geometric algebra the general decomposition of SU(2) gauge potential on the sphere bundle of a compact and oriented 4-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) $. And one can 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 Chren density is a topological invariant, the sum topological chargers of the branches will remain constant during the bifurcation process.
Duan Yishi
Fu Libin
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