On the hyperbolicity of Maxwell's equations with a local constitutive law

Perlick, Volker

doi:10.1063/1.3579133

Cited by 31 publications

(27 citation statements)

References 27 publications

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“…This excludes some degenerate cases which are hardly of physical interest. Then the characteristic equation is equivalent to (which is up to conformal transformations in agreement with the results of Novello et al [22]) (27) and is sometimes called the "light-cone condition" (compare for example [24]). Generalizing a standard terminology from electrodynamics in media, a ik 1 and a ik 2 are called the optical metrics of the vacuum in the L(F, G) theory.…”

Section: B Three-dimensional Notation Of Field Equationssupporting

confidence: 67%

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Testing nonlinear vacuum electrodynamics with Michelson interferometry

2015

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We discuss the theoretical foundations for testing nonlinear vacuum electrodynamics with Michelson interferometry. Apart from some nondegeneracy conditions to be imposed, our discussion applies to all nonlinear electrodynamical theories of the Plebański class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to nonlinear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental setups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and to rotate it. If an electromagnetic field is placed in one arm, the interferometer could have the size of a gravitational wave detector, i.e., an arm length of several hundred meters. If the whole interferometer is placed in an electromagnetic field, one would have to do the experiment with a tabletop interferometer. As an alternative to a traditional Michelson interferometer, one could use a pair of optical resonators that are not bigger than a few centimeters. Then the whole apparatus would be placed in the background field and one would either compare the situation where the field is switched on with the situation where it is switched off or one would rotate the apparatus with the field kept switched on. We derive the theoretical foundations for these types of experiments, in the context of an unspecified nonlinear electrodynamics of the Plebański class, and we discuss their feasibility. A null result of the experiment would place bounds on the parameters of the theory. We specify the general results to some particular theories of the Plebański class; in particular, we give numerical estimates for Born, Born-Infeld and Heisenberg-Euler theories.

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Section: B Three-dimensional Notation Of Field Equationssupporting

confidence: 67%

“…The general method goes back to Luneburg and is outlined, e.g., for electrodynamics in ordinary media, in the book by Kline and Kay [26]. For a discussion in a more general context, which includes the case to be considered here, we refer to Perlick [27].…”

Section: B Three-dimensional Notation Of Field Equationsmentioning

confidence: 99%

Testing nonlinear vacuum electrodynamics with Michelson interferometry

2015

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“…Usually a wave is represented by a plane wave ansatz or by its generalization in series, see [43], [44] for a modern review of this non-covariant approach. Instead, we will apply the following covariant description that is similar to what is given in [45] and [46].…”

Section: A Generalized Wavefront and Characteristic Systemmentioning

confidence: 99%

“…Our aim is to understand the possible new physical phenomena coming from the additional electromagnetic parameters. Recently there has been considerable progress in this area, [27], [28], [29], [30], [32], [33], [34], [35], [37], [38], [41], [42], [44]. Here we are interested mostly in the skewon effects on the light cone structure.…”

Section: Introductionmentioning

confidence: 99%

Skewon modification of the light cone structure

Itin

2015

Phys. Rev. D

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Electromagnetic media with generic linear response provide a rich class of Lorentz violation models. In the framework of a general covariant metric-free approach, we study electromagnetic wave propagation in these media. We define the notion of an optic tensor and present its unique canonical irreducible decomposition into the principle and skewon parts. The skewon contribution to the Minkowski vacuum is a subject that does not arise in the ordinary models of Lorentz violation based on a modified Lagrangian. We derive the covector parametrization of the skewon optic tensor and discuss its U (1)-gauge symmetry. We obtain several compact expressions for the contribution of the principle and skewon optic tensor to the dispersion relation. As an application of the technique proposed here, we consider the case of a generic skewon tensor contributed to a simple metric-type principle part. Our main result: Every solution of the skewon modified Minkowski dispersion relation is necessary spacelike or null. It provides an extreme violation of the Lorentz symmetry. The case of the antisymmetric skewon is studied in detail and some new special cases (electric, magnetic, and degenerate) are discovered. In the case of a skewon represented by a symmetric matrix, we observe a parametric gap that has some similarity to the Higgs model. We worked out a set of specific examples that justify the generic properties of the skewon models and demonstrate the different types of the Lorentz violation phenomena.

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“…The vacuum admittance ε 0 /µ 0 = e 2 /(2hα) can be expressed in terms of the fine structure constant α, the elementary charge e and Planck's constant h. The possible time variability of the vacuum impedance and the fine structure constant were discussed by Tobar [80] and us. 10) New initial value formulation of Maxwell's theory by Perlick: It was studied by Perlick [66] for the premetric version. He derived several conditions for the evolution equations to be hyperbolic, strongly hyperbolic, or symmetric hyperbolic.…”

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confidence: 99%

Generally covariant Maxwell theory for media with a local response: Progress since 2000

Hehl

Itin

Obukhov

2016

2016 URSI International Symposium on Electromagnetic Theory (EMTS)

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Abstract-In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure of electrodynamics (conservation of electric charge and magnetic flux). Moreover, it is ideally suited for applying it to media with local (and mainly linear) response behavior. We try to collect the new knowledge that grew out of this development. We would like to ask the participants of EMTS 2016 to inform us of work that we may have overlooked in our review. If the medium has a local and linear response behavior, the excitation H = (H, D) is local and linear in the field strength F = (E, B). In components we havěHere i, j, ... = 0, 1, 2, 3 andȞ ij := (1/2)ǫ ijkl H kl . The response tensor density χ has 36 independent components. It can be decomposed into three irreducible pieces with 36 = 20 + 15 + 1 components, respectively. Split in (1+3) dimensions, with a, b, .. = 1, 2, 3, we have (for details, see [18], [24])Up to here, the metric of spacetime, that is, the gravitational potential, did not enter anywhere. We have a premetric B D

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On the hyperbolicity of Maxwell's equations with a local constitutive law

Cited by 31 publications

References 27 publications

Testing nonlinear vacuum electrodynamics with Michelson interferometry

Testing nonlinear vacuum electrodynamics with Michelson interferometry

Skewon modification of the light cone structure

Generally covariant Maxwell theory for media with a local response: Progress since 2000

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