中国物理B ›› 2009, Vol. 18 ›› Issue (5): 1814-1820.doi: 10.1088/1674-1056/18/5/016

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Knot solitons in AFZ model

任继荣, 墨淑凡, 朱涛   

  1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2008-09-02 修回日期:2008-10-10 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:
    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).

Knot solitons in AFZ model

Ren Ji-Rong(任继荣)†, Mo Shu-Fan(墨淑凡)‡, and Zhu Tao(朱涛)\S   

  1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China
  • Received:2008-09-02 Revised:2008-10-10 Online:2009-05-20 Published:2009-05-20
  • Supported by:
    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).

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摘要： 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 π3(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.

关键词: knot theory, solitons, topology, AFZ model

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.

Key words: knot theory, solitons, topology, AFZ model

中图分类号:  (Nonlinear or nonlocal theories and models)

  • 11.10.Lm
11.15.-q (Gauge field theories) 02.40.Pc (General topology)