Abstract
AbstractPersistent topological structures in physical systems have become increasingly important over the last years. Electromagnetic fields with knotted field lines play a special role among these, since they can be used to transfer their knottedness to other systems like plasmas and quantum fluids. In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time, so that all knotted closed field lines maintain their knot type. We use an approach due to Bateman to prove that for every link L there is such an electromagnetic field that satisfies Maxwell’s equations in free space and that has closed electric and magnetic field lines in the shape of L for all time. The knotted and linked field lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference41 articles.
1. Adams, C.C.: The Knot Book. W.H. Freeman and Company, New York (1994)
2. Atiyah, M.: The Geometry and Physics of Knots. Cambridge University Press, Cambridge (1990)
3. Bateman, H.: The Mathematical Analysis of Electrical and Optical Wave-Motion. Dover, New York (1915)
4. Berry, M.V.: Knotted zeros in the quantum states of hydrogen. Found. Phys. 31, 659–667 (2001)
5. Bialynicki-Birula, I.: New solutions of the Dirac, Maxwell, and Weyl equations from the fractional Fourier transform. Phys. Rev. D 103, 085001 (2021)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献