Foundations of Classical Electrodynamics

Hehl, Friedrich W.; Obukhov, Yuri N.

doi:10.1007/978-1-4612-0051-2

Cited by 640 publications

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“…Moreover, as we have shown [20,25], we find the correct Lorentzian signature. The Lorentzian (also known as Minkowskian) signature can be traced back to the Lenz rule, which determines the sign of theḂ term in the induction law.…”

Section: Vanishing Birefringencesupporting

confidence: 75%

“…2. Faraday-Schouten pictograms of the electromagnetic field, see [20]. The electric excitation D is a twisted 2-form, the magnetic excitation H a twisted 1-form.…”

Section: Charge Active: Excitationmentioning

confidence: 99%

“…In the meantime we learnt from the literature that appeared since 2003 (see, e.g., Delphenich [8,9], Itin [24], Kaiser [26], Kiehn [29], and Lindell & Sihvola [35,37]) and improved our derivation of the light cone, simplified it, made it more transparent (see, e.g., [21,23,33,45,46]). The formalism and the conventions we take from [20].…”

Section: Introductionmentioning

confidence: 99%

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Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Hehl

Obukhov

Lecture Notes in Physics

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Summary. We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral matter. Electric charge and magnetic flux are postulated to be conserved. As a consequence, the inhomogeneous and the homogeneous Maxwell equations emerge expressed in terms of the excitation H = (H, D) and the field strength F = (E, B), respectively. H and F are assumed to fulfill a local and linear "spacetime relation" with 36 constitutive functions. The propagation of electromagnetic waves is considered under such circumstances in the geometric optics limit. We forbid birefringence in vacuum and find the light cone including its Lorentzian signature. Thus the conformally invariant part of the metric is recovered. If one sets a scale, one finds the pseudo-Riemannian metric of spacetime.

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Section: Vanishing Birefringencesupporting

confidence: 75%

“…2. Faraday-Schouten pictograms of the electromagnetic field, see [20]. The electric excitation D is a twisted 2-form, the magnetic excitation H a twisted 1-form.…”

Section: Charge Active: Excitationmentioning

confidence: 99%

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Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Hehl

Obukhov

Lecture Notes in Physics

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“…In order to understand the coupling of electromagnetism to gravity, it is most convenient and reasonable to start from the premetric formulation of the electrodynamical theory. Following the early work of Kottler, Cartan, and van Dantzig, one can indeed develop an axiomatic approach to the electromagnetic field [3,4,5] without assuming any specific geometric structure beyond the differentiable structure of the spacetime manifold, see also [6,7]. At the heart of this approach, there are the well established experimental facts (that can be formulated as fundamental axioms) of electric charge and magnetic flux conservation.…”

Section: Premetric Formulation Of Electrodynamicsmentioning

confidence: 99%

“…For example, it can be nonlinear and even nonlocal. The nonlinearity can be fundamental or effective, see the discussion in [3]. Here we will limit our attention to the linear spacetime relations.…”

Section: Premetric Formulation Of Electrodynamicsmentioning

confidence: 99%

Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

Hehl

Obukhov

2008

Gen Relativ Gravit

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The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge "substratum" and the flux "substratum"are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the spacetime relation H = H(F ) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F , is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.

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