Condensed Matter Seminar: Knots in Electromagnetism, fluid dynamics and non abelian gauge theories

Surprisingly, Maxwell's equations admit a class of infinitely many knot solutions for null fields (E^2=B^2, E\cdot B=0). The prototype is the Hopfion solution. There are 4 types of conserved helicities that characterize the knots. I will describe these topologically non-trivial solutions using Bateman's formulation and present a novel way to derive them based on special conformal transformations. The E.M knots can be mapped into knots in fluid dynamics. The Euler theory coupled to E.M background admits a non-trivial helicity and correspondingly knot solutions. Finally, I will show that for null non-abelian fields there are conserved helicities. I will describe attempts to construct YM knots.