Abstract This paper studies the topological properties of knotted solitons in the (3+1)-dimensional Aratyn--Ferreira--Zimerman (AFZ) model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group $\pi$3(S3)=Z. By making use of the decomposition of U(1) gauge potential theory and Duan's topological current theory, it is shown that the invariant is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes (splitting, merging and intersection) of these knot vortex lines.
Received: 02 September 2008
Revised: 10 October 2008
Accepted manuscript online:
Fund: Project supported by the
National Natural Science Foundation of China (Grant No 10275030) and
the Cuiying Program of Lanzhou University, China (Grant No
22500-582404).
Cite this article:
Ren Ji-Rong(任继荣), Mo Shu-Fan(墨淑凡), and Zhu Tao(朱涛) Knot solitons in AFZ model 2009 Chin. Phys. B 18 1814
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