The topological quantization and the branch process of the (k-1)-dimensional topological defects

Details The topological quantization and the branch process of the (k-1)-dimensional topological defects The topological quantization and the branch process of the (k-1)-dimensional topological defects

1998-10-15

arxiv.org/abs/hep-th/9810111v1

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, no figure, LATEX file

Scientific paper

In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian $J(\phi/v) \neq 0$. When $J(\phi/v)=0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function $\vec \phi$ but the total charge of the topological defects is still unchanged.

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