Multipole theory and the Hehl–Obukhov decomposition of the electromagnetic constitutive tensor

Lange, O. L. de; Raab, R. E.

doi:10.1063/1.4919545

Cited by 4 publications

(6 citation statements)

References 25 publications

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“…Eventually, the hypothetical skewon piece [35] carries 3 permittivities n a , the 3 permeabilities m a , and the 9 magnetoelectric pieces s a b . Equivalent response relations were formulated by Serdyukov et al [92, p.86] and studied in quite some detail, see also de Lange and Raab [52].…”

Section: A Local and Linear Electromagnetic Responsementioning

confidence: 99%

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Hehl

2016

Fundamental Theories of Physics

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We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. -In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density χ i jkl = −χ jikl = −χ i jlk with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in χ i jkl , it can be derived from it.file CarlBrans80 08.This gauging of the P(1, 3) extends the geometrical framework of gravity. The 4 translational potentials e i α and the 6 Lorentz potentials Γ i αβ = −Γ i β α span a Riemann-Cartan spacetime, enriching the Riemannian spacetime of GR by the presence of Cartan's torsion; here α, β = 0, 1, 2, 3 are (anholonomic) frame indices. Whereas the translational potentials couple to the canonical energy-momentum ten-2 We skip here the plethora of scalar mesons, π ± , π 0 , η, f 0 (500), η ′ (958), f 0 (980), a 0 (980), ...,they are all composed of two quarks. Thus, the scalar mesons do not belong to the fundamental particles.

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Section: A Local and Linear Electromagnetic Responsementioning

confidence: 99%

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Hehl

2016

Fundamental Theories of Physics

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“…Remark 2: If V out were to be occupied by a homogeneous, linear, bianisotropic material different from the one occupying V in , the process of deriving Eqs. (8) and (13) shows that the Post constraint would apply to that material too.…”

Section: Natural Emergence Of the Post Constraintmentioning

confidence: 99%

“…As boundary conditions, let us use Eqs. (13) without assuming that S is charge neutral and current neutral; i.e.,…”

Section: Surface Statesmentioning

confidence: 99%

“…(4) without considering that the redundancies possibly contained in constitutive equations could be filtered out by the Maxwell equations when applied separately to V in and V out . When the redundancy in the form of Ψ was filtered out by the Maxwell equations on application to V in , we obtained the boundary conditions (13) [21]. Thus, Ψ does not have a recognizable existence in either V in or V out and it does not enter the boundary conditions.…”

Section: Natural Emergence Of the Post Constraintmentioning

confidence: 99%

“…A simple boundaryvalue problem has been formulated to show that Ψ is measurable [6]. Multipole symmetry arguments have been derived to rule against as well as for the Post constraint [11][12][13]. Data from scattering experiments conducted on a single "Tellegen particle" were produced to show that Ψ exists [14], but those data-while sufficient to establish the magnetoelectric phenomenon (which is not in doubt)-are insufficient to invalidate the Post constraint.…”

Section: Introductionmentioning

confidence: 99%

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Axions, surface states, and the post constraint in electromagnetics

Lakhtakia

Mackay

2015

SPIE Proceedings

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After formulating the frequency-domain Maxwell equations for a homogeneous, linear, bianisotropic material occupying a bounded region, we found that the axionic piece vanishes from both the differential equations valid in the region and the boundary conditions, thereby vindicating the Post constraint. Our analysis indicates that characteristic effects that may be observed experimentally with magnetoelectric materials are not the consequences of the axionic piece but of an admittance that describes surface states.

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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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Multipole theory and the Hehl–Obukhov decomposition of the electromagnetic constitutive tensor

Cited by 4 publications

References 25 publications

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Axions, surface states, and the post constraint in electromagnetics

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

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