TY - JOUR

T1 - New knotted solutions of Maxwell's equations

AU - Hoyos, Carlos

AU - Sircar, Nilanjan

AU - Sonnenschein, Jacob

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd.

PY - 2015/6/26

Y1 - 2015/6/26

N2 - In this paper 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 obtain a wide class of solutions from the basic configuration, such as constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of 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 the charge takes integer values.

AB - In this paper 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 obtain a wide class of solutions from the basic configuration, such as constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of 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 the charge takes integer values.

KW - abelian-non abelian map

KW - classical electrodynamics

KW - complex conformal transformation

KW - knots

KW - quaternions

KW - topological solutions

UR - http://www.scopus.com/inward/record.url?scp=84930959644&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/25/255204

DO - 10.1088/1751-8113/48/25/255204

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AN - SCOPUS:84930959644

SN - 1751-8113

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 25

M1 - 255204

ER -