The fundamental equations of electromagnetism, independent of metrical geometry

Dantzig, D. van

doi:10.1017/s0305004100012664

Cited by 86 publications

(91 citation statements)

References 3 publications

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“…Inside the vacuum regions, the solutions of Maxwell's equations are well known: the angular variation of the electric field is a sum of complex exponentials, characterized by indices ν I and ν III , whereas the radial dependence obeys the Bessel equation. The radial dependence of the electric field can therefore be written as a sum of Bessel functions J ν and Y ν or as a sum of Hankel functions H (1) ν and H (2) ν . In the inner region (I), we decompose the field using the Bessel functions where we can reject the Bessel function Y ν , because it has a singularity at the origin.…”

Section: Transforming Space To Confine Light (A) Dielectric Microresomentioning

confidence: 99%

“…In the inner region (I), we decompose the field using the Bessel functions where we can reject the Bessel function Y ν , because it has a singularity at the origin. In the surrounding vacuum region (III), we decompose using the Hankel functions, where we can drop the Hankel function H (2) ν , which represents an incoming wave:…”

Section: Transforming Space To Confine Light (A) Dielectric Microresomentioning

confidence: 99%

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Transformation optics beyond the manipulation of light trajectories

Ginis

Tassin

2015

Phil. Trans. R. Soc. A.

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Section: Transforming Space To Confine Light (A) Dielectric Microresomentioning

confidence: 99%

Section: Transforming Space To Confine Light (A) Dielectric Microresomentioning

confidence: 99%

Transformation optics beyond the manipulation of light trajectories

Ginis

Tassin

2015

Phil. Trans. R. Soc. A.

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“…In (7.2) and (7.3) there enter the canonical energy-momentum and hypermomentum currents of matter Σ α and ∆ α β , the gravitational gauge field momenta 4) and the canonical energy-momentum and hypermomentum currents of the gauge fields…”

Section: An Electric Charge In Einstein-dilation-shear Gravitymentioning

confidence: 99%

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

Puntigam

Lämmerzahl

Hehl

1997

Class. Quantum Grav.

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The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck. file vandyck8.tex, 1997-02-11, Classical and Quantum Gravity, to be published (1997)

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“…This fact was recognized long ago [10], [11], [12], [13], but its comprehensive treating was provided only recently, see [5] and the references given therein. In vacuum, the metric-independence of the Maxwell system is just a nice mathematical property, but in electromagnetism of media this fact has a firm physical meaning.…”

Section: Introductionmentioning

confidence: 99%

Covariant jump conditions in electromagnetism

Itin

2012

Annals of Physics

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A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants.

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The fundamental equations of electromagnetism, independent of metrical geometry

Cited by 86 publications

References 3 publications

Transformation optics beyond the manipulation of light trajectories

Transformation optics beyond the manipulation of light trajectories

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

Covariant jump conditions in electromagnetism

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