Non-dissipative electromagnetic media with two Lorentz null cones

Dahl, Matias F.

doi:10.1016/j.aop.2012.11.005

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…Finally, the surface has mirror symmetry with respect to a plane determined by the origin and two singular points. It appears to be finite for the case e φ /|ε| < 1/2 (see figure 3 When ε = 0, the wave surface transforms to the set of two planes, n x = 1 and n y sin ψ = n z cos ψ. and (c) describe the cases exp(2φ) < |ε/2q 3 |, exp(2φ) = |ε/2| and exp(2φ) > |ε/2| respectively; the plot on panel (a) has similar form as in [60]. All these surfaces possess rotational symmetry.…”

Section: Type IIImentioning

confidence: 90%

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Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

Balakin

Zayats

2018

Class. Quantum Grav.

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We construct a classification of dispersion relations for the electromagnetic waves non-minimally coupled to the space-time curvature, based on the analysis of the susceptibility tensor, which appears in the non-minimal Einstein-Maxwell theory. We classify solutions to the Fresnel equation for the model with a trace-free non-minimal susceptibility tensor according to the Petrov scheme. For all Petrov types we discuss specific features of the dispersion relations and plot the corresponding wave surfaces.

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Section: Type IIImentioning

confidence: 90%

“…FIG.1: Axial cross-section of the wave surfaces for the type N. The panels (a), (b), and (c) describe the cases exp(2φ) < |ε/2q3|, exp(2φ) = |ε/2|, and exp(2φ) > |ε/2|, respectively, the plot on the panel (a) has the similar form as in[60]. All these surfaces possess the rotation symmetry.…”

mentioning

confidence: 95%

Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

Balakin

Zayats

2018

Class. Quantum Grav.

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“…The two optical axes are lying in the plane q 2 = 0, the fourth coordinate q 3 is suppressed. In contrast, double cone media for vanishing skewon piece have been investigated by Dahl and Favaro [55,56].…”

Section: In Premetric Electrodynamicsmentioning

confidence: 99%

The Kummer tensor density in electrodynamics and in gravity

et al. 2014

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Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K ijkl . This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T ijkl , which is antisymmetric in its first two and its last two indices:If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as 1 defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R ijkl of a Riemann-Cartan spacetime, then K ∼ R 3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4, R) and, subsequently, under the Lorentz group SO(1, 3).

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“…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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Non-dissipative electromagnetic media with two Lorentz null cones

Cited by 8 publications

References 30 publications

Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

The Kummer tensor density in electrodynamics and in gravity

Skewon modification of the light cone structure

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