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

Duan, Yishi; Jiang, Ying; Yang, Guohong

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

Authors

Duan, Yishi

Jiang, Ying

Yang, Guohong

Description

In the light of $ϕ$-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 $J(ϕ/v) \neq 0$. When $J(ϕ/v)=0$, 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 $\vec ϕ$ but the total charge of the topological defects is still unchanged.
17 pages, no figure, LATEX file