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...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 invariazat 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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No 10275030)the Cuiying Program of Lanzhou University,China(Grant No 22500-582404)
文摘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 invariazat 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.
