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from Part I - General Properties of Fields; Scalars and Gauge Fields
Published online by Cambridge University Press: 04 March 2019
In this chapter, we study the Hopfion solution of electromagnetism. It is a solution characterized by a topological number, the Hopf index, associated with the Hopf map from the 3-sphere to the 2-sphere (Hopf fibration). It is also characterized by nonzero “helicities,” which are defined as integrals of Chern–Simons forms on the spatial volume, as well as having a knot structure, where the electric and magnetic fields are linked, with nonzero linking number. Generalization of these electromagnetic knots are also given.
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