Condensed Matter Seminar: Knoted solutions of free Maxwell's equations

Abstract:

In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. I will first present the Bateman' formulation of EM and demonstrate the solution in terms of the prototype Hopfion solution.

I will describe  a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions.

This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves.

We have introduced a covariant formulation of the Bateman’s construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities.

We have also given a formulation in terms of quaternions.  This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of SU(2) gauge theory.  We have computed the corresponding Chern-Simons charge in a class of solutions and it takes integer values.

Event Organizer: Prof. Eli Eisenberg