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arXiv · 1502.01382

New knotted solutions of Maxwell's equations

Carlos Hoyos·Nilanjan Sircar·Jacob Sonnenschein
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Abstract

In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such 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. 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 CS charge in a class of solutions and it takes integer values.

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Carlos Hoyos, Nilanjan Sircar, Jacob Sonnenschein. 2015-02-04. New knotted solutions of Maxwell's equations. https://doi.org/10.1088/1751-8113/48/25/255204

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