Abstract

In this talk I will describe topologically non-trivial solutions of vacuum electrodynamics. A prototype solution of this class is the Hopfion. I will present a novel method of generating such null solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman’s variables. This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves. I will introduce a covariant formulation of the Bateman’s construction and discuss the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. I will further present 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 of a class of such connection.