The Kummer tensor density in electrodynamics and in gravity

Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

doi:10.1016/j.aop.2014.06.007

Cited by 24 publications

(38 citation statements)

References 59 publications

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“…In Sec.5, we will study the propagation of gravitational waves in TG within the geometric optics approximation. We will follow the procedure that we developed for electrodynamics [2,22,29]. Since in TG we have four generators of the gauge group, things become a bit more complicated than in electrodynamics.…”

Section: Reversibilitymentioning

confidence: 99%

“…We may call [1] χ a reversible symmetric principal part (principal-1), [4] χ a reversible antisymmetric principal part (principal-2), [5] χ a reversible axion (axion-1); likewise we may call [2] χ a skewon antisymmetric principal part (skewon-1), [3] χ a skewon symmetric principal part (skewon-2), and [6] χ a skewon axion (axion-2). This is summarized in Table 1.…”

Section: S 4 × S 2 Decomposition Of χ αβ µ γδ νmentioning

confidence: 99%

“…Disp. [1] χ αβ γ µν ρ principal-1 yes yes yes [2] χ αβ γ µν ρ skewon-1 no yes yes [3] χ αβ γ µν ρ skewon-2 no yes yes [4] χ αβ γ µν ρ principal-2 yes yes yes [5] χ αβ γ µν ρ axion-1 yes no no [6] χ αβ γ µν ρ axion-2 no yes no ofχ αβ µγδ ν :…”

Section: S 6 Decomposition Ofχ αβ µγδ νmentioning

confidence: 99%

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Premetric teleparallel theory of gravity and its local and linear constitutive law

et al. 2018

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We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity.

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Section: Reversibilitymentioning

confidence: 99%

Section: S 4 × S 2 Decomposition Of χ αβ µ γδ νmentioning

confidence: 99%

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Premetric teleparallel theory of gravity and its local and linear constitutive law

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“…A common way to derive such a decomposition is to apply the Young diagram technique. A brief account of this subject is given in [56]. Note that a generic 4-rank tensor (without additional symmetries) is canonically decomposed into five sub-tensors.…”

Section: Constitutive Pseudotensormentioning

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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“…11) The Kummer tensor of electrodynamics, Fresnel wave surfaces unmasked as Kummer surfaces: We found a fourth rank Kummer tensor density [3] that is cubic in the response tensor χ,…”

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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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The Kummer tensor density in electrodynamics and in gravity

Cited by 24 publications

References 59 publications

Premetric teleparallel theory of gravity and its local and linear constitutive law

Premetric teleparallel theory of gravity and its local and linear constitutive law

Skewon modification of the light cone structure

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

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