Knot solitons in AFZ model |
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| Authors: | Ren Ji-Rong Mo Shu-Fan and Zhu Tao |
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| Affiliation: | Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China |
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| 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
$\pi_3(S^3)=Z$. 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. |
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| Keywords: | knot theory solitons topology AFZ model |
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