Spinors and Pre-Metric Electromagnetism

Delphenich, D. H.

doi:10.1007/s00006-008-0115-6

Cited by 6 publications

(14 citation statements)

References 17 publications

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“…The premetric approach of electrodynamics has also been developed over the years by Delphenich [30,31,32] and, more recently, by Cabral & Lobo [18]. Rumpf [144] and Zhang et al [176], for instance, discuss realistic engineering applications for (110,111), but without using the the skewon part.…”

Section: (109)mentioning

confidence: 99%

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Hehl

Itin

Obukhov

2016

Int. J. Mod. Phys. D

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In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical * Based on an invited talk given at the Annual Meeting of the German Physical Society (DPG) in Berlin on 20 March 2015, "Working Group on Philosophy of Physics (AGPhil)". We sincerely thank Dennis Lehmkuhl (Wuppertal, now Pasadena) and his co-organizers Meinard Kuhlmann (Mainz) and Wolfgang Pietsch (Munich) [92] for the invitation. In the present version, we appreciably enriched our text by adding more formalism. We apologize to the philosophers for any inconvenience. A short version of this paper will be submitted to the International Journal of Modern Physics D.

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Section: (109)mentioning

confidence: 99%

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Hehl

Itin

Obukhov

2016

Int. J. Mod. Phys. D

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“…The q i are the components of the wave vector of the light. 9 If birefringence is forbidden, then the light cone emerges [30], that is, the metric g ij up to a (dilation) factor [19]. Let us come back to χ ijkl .…”

Section: Constitutive Relationmentioning

confidence: 99%

“…The covariant epsilon-system is marked by a hat:ˆ ijkl = ±1, 0;ˆ 0123 = +1. 9 This scheme was generalized to Abelian gauge and string theory by Schuller, Wohlfahrt, et al, see the articles [49,53] and the references given there. Also in these generalized schemes a Tamm-Rubilar type tensor plays a decisive role.…”

Section: Constitutive Relationmentioning

confidence: 99%

“…Using modern notation, including the summation convention, see Schouten [52], we can rewrite (8) and (9) as…”

Section: Introductionmentioning

confidence: 99%

“…The only exception is that we denote the field strength by F in order not to mix it up with Minkowksi's F . For other presentations of Maxwell's equations in exterior calculus, see, e.g., Bamberg & Sternberg [5], , Delphenich [8,9], Frankel [14], Jancewicz [27], Lindell [34], Misner, Thorne & Wheeler [41], Russer [51], Thirring [60], and Trautman [61]. 3 We call a structure premetric, if it can be defined "before" a metric is available (or a metric exists, but it is not used).…”

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confidence: 99%

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Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor

Hehl¹

2008

Ann. Phys.

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In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4-dimensional form: lor f = −s, lor F * = 0. Here 'lor', an abbreviation of Lorentz, represents the 4-dimensional differential operator. We study Minkowski's derivation and show how these equations generalize to their modern premetric form in the framework of tensor and exterior calculus. After mentioning some applications of premetric electrodynamics, we turn to Minkowski's discovery of the energy-momentum tensor of the electromagnetic field. We discuss how he arrived at it and how its premetric formulation looks like.

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Symmetries and pre‐metric electromagnetism

Delphenich

2005

Annalen der Physik

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The equations of pre‐metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2‐forms over the spacetime manifold. The general form for the symmetry equations of the system is computed and then specialized to various possible forms for an electromagnetic constitutive law, namely, uniform linear, non‐uniform linear, and uniform nonlinear. It is shown that in the uniform linear case, one has four possible ways of prolonging the symmetry Lie algebra, including prolongation to a Lie algebra of infinitesimal projective transformations of a real four‐dimensional projective space. In the most general non‐uniform linear case, the effect of non‐uniformity on symmetry seems inconclusive in the absence of further specifics, and in the uniform nonlinear case, the overall difference from the uniform linear case amounts to a deformation of the electromagnetic constitutive tensor by the electromagnetic field strengths, which induces a corresponding deformation of the symmetry Lie algebra that was obtained in the linear uniform case.

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Spinors and Pre-Metric Electromagnetism

Cited by 6 publications

References 17 publications

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor

Symmetries and pre‐metric electromagnetism

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