Knotted Topological Phase Singularities of Electromagnetic Field

Abstract

In this paper, knotted objects (RS vortices) in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the $\varphi$-mapping topological current theory proposed by Prof. Duan, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.

6 pages, no figures, author's name have been corrected

References in corpus (9)

• Vortex lines of the electromagnetic field
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• Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
• Helicity, polarization, and Riemann-Silberstein vortices
• Inner topological structure of Hopf invariant
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Cited by in corpus (3)

• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Knots and the Maxwell Equations
• The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave