Knots in interaction

Abstract

We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting and adjoining is governed by a four-point vertex in combination with duality transformations. The total linking number is preserved during the interaction. It receives contributions both from the twist and the writhe, which are variable. Therefore solitons can twine and coil and links can be formed.

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References in corpus (4)

• Partially Dual variables in SU(2) Yang-Mills Theory
• To be or knot to be?
• Faddeev-Hopf knots: Dynamics of linked un-knots
• Partial duality in SU(N) Yang-Mills theory

Cited by in corpus (8)

• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Dual neutral variables and knot solitons in triplet superconductors
• Knotlike Cosmic Strings in The Early Universe
• Topological aspects of dual superconductors
• Semiclassical Quantization of Hopf Solitons
• Exact knot solutions in a generalized Skyrme-Faddeev model
• Novel Topological Invariant in the U(1) Gauge Field Theory
• Skyrme-Faddeev Lagrangian from reformulated Georgi-Glashow model