Electromagnetic Duality, Charges, Monopoles, Topology, ...

Mignaco, J. A.

doi:10.1590/s0103-97332001000200014

Cited by 18 publications

(8 citation statements)

References 27 publications

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“…which leaves us with one transformation parameter ϕ, only. In the form (25) and (28), the transformation was introduced by Larmor as duality rotation [17,18]. Applying (27) and (28), the GBC conditions (1) are transformed to…”

Section: Duality Transformationmentioning

confidence: 99%

Self-Dual Boundary Conditions in Electromagnetics

Lindell¹,

Sihvola²

2020

PIER

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Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is studied. Expressing the boundary conditions in terms of a generalized impedance dyadic, the self-dual boundaries fall in two sets depending on symmetry or antisymmetry of the impedance dyadic. Previously known cases are found to appear as special cases of the general theory. Plane-wave reflection from boundaries defined by each of the two cases of selfdual conditions are analyzed and waves matched to the corresponding boundaries are determined. As a numerical example, reflection from a special case, the self-dual EH boundary, is computed for two planes of incidence.

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Section: Duality Transformationmentioning

confidence: 99%

Self-Dual Boundary Conditions in Electromagnetics

Lindell¹,

Sihvola²

2020

PIER

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“…To inject some physics into these thus far formal results, it is helpful to notice that Maxwell's eq.s(2.8) will remain invariant under formal replacement: E → −B, B → E. These are the electric-magnetic duality transformations discovered by Heviside in 1893 as described in the paper by Mignaco (Mignaco 2001). Maxwell's equations with charges and currents loose this type of invariance, unless the magnetic monopoles are present.…”

Section: Some Basic Facts About Instantonsmentioning

confidence: 99%

Optical knots and contact geometry I. From Arnol’d inequality to Ranada’s dyons

Kholodenko

2015

Anal.Math.Phys.

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Recently there had been a great deal of activity associated with various schemes of designing both analytical and experimental methods describing knotted structures in electrodynamics and in hydrodynamics. The majority of works in electrodynamics were inspired by the influential paper by Ranada (1989) and its subsequent refinements. In this work and in its companion we reanalyze Ranada's results using methods of contact geometry and topology. Not only our analysis allows us to reproduce his major results but, in addition, it provides opportunities for considerably extending the catalog of known knot types. Furthermore, it allows to reinterpret both the electric and magnetic charges purely topologically thus opening the possibility of treatment of masses and charges in Yang-Mills and gravity theories also topologically. According to (now proven) Thurston's geometrization conjecture complements of all knots/links in S 3 are spaces of positive, zero or negative curvature. This means that spaces around our topological masses/charges are curved. This fact is essential for design of purely topological theories of gravity, electromagnetism and strong/weak interactions.

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“…The Maxwell equations with charge sources are invariant under the following electromagnetic duality transformation [16,17]:…”

Section: Duality Transformationmentioning

confidence: 99%

Thomas-BMT equation generalized to electric dipole moments and field gradients

Metodiev

2015

Preprint

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An expression is presented for the relativistic equations of motion, including field gradients, of a particle and its spin with electric and magnetic dipole moments aligned along the spin axis. An electromagnetic duality transformation is used to generalize a Thomas-BMT equation with gradient terms. Corrections to particle dynamics in storage rings for precision (g − 2) and electric dipole moment measurements are calculated, and applications to precision particle tracking programs are considered.

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Electromagnetic Duality, Charges, Monopoles, Topology, ...

Cited by 18 publications

References 27 publications

Self-Dual Boundary Conditions in Electromagnetics

Self-Dual Boundary Conditions in Electromagnetics

Optical knots and contact geometry I. From Arnol’d inequality to Ranada’s dyons

Thomas-BMT equation generalized to electric dipole moments and field gradients

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