Optical helicity and Hertz vectors

Elbistan, Mahmut

doi:10.1016/j.physleta.2018.05.012

Cited by 5 publications

(3 citation statements)

References 35 publications

(106 reference statements)

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“…We will consider here only the original zilch introduced by Lipkin, a conserved current of dimension five. While a physical interpretation of the zilch remained obscure for a long time, recently it was shown that the zilch measures the asymmetry in the interaction of the electromagnetic field with small chiral molecules [26] similarly to the effects of the optical helicity on chiral and magnetoelectric media [27,28] and Weyl semimetals [30]. We therefore take the zilch as a legitimate local measure of the helicity of light.…”

Section: Introductionmentioning

confidence: 99%

Zilch vortical effect

2018

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We study the question if a helicity transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant "zilch" current. In order to avoid problems of causality, we quantize the system on a cylinder of a finite radius and then discuss the limit of infinite radius. We find that net helicityand zilch currents are only generated in the case of the finite radius and are due to duality violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the wellknown temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies. arXiv:1807.10705v1 [hep-th] 27 Jul 2018 (T E,T M ) J = ωA (T M,T E) J .We can therefore introduce eigenvectors of the curl operatorwith the eigenvaluesIn terms of electric and magnetic fields these modes fulfill the relationswhich show that these modes correspond to left-and right-circularly polarized electromagnetic fields. The gauge potential can now be quantized in this basis as follows:with ω 2 J = k 2 z + k 2 ⊥ as in Eq. (25). The projection of the angular momentum on the z axis can be computed from the expression of the Poynting vector P = i 2 E × E † as3 x : h := J α (+) † J α (+) J − α (−) † J α (−) J , (72) Q ζ = d 3 x : ζ := J ω 2 J α (+) † J α (+) J − α (−) † J α (−) J

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Section: Introductionmentioning

confidence: 99%

Zilch vortical effect

2018

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“…There are electromagnetic problems that cannot be solved or are complicated to elaborate without the Hertz vector [26]. The symmetry of the Maxwell equations allow an alternative introduction of the Hertz vector involving its gauge symmetries [27][28][29]. Ornigotti et al showed that due to the transversality of the electromagnetic wave, the Hertz vector can be expressed as a product of a constant polarization vector and a scalar potential [30].…”

Section: Generalized Vector Potential Hertz Vector and Modified Loren...mentioning

confidence: 99%

Generalized Hertz Vector in the Dissipative Electrodynamics

Gambár¹,

Márkus²

2023

WJP

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In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve particular radiation processes. It indicates that the related method is sometimes more effective than the scalar and vector potential-based relations. Finally, the measurable field variables, the electric and magnetic fields, can be deduced by direct calculation from the Hertz vector. However, right now, the introduction of the Hertz vector operates if the conductive current density j = 𝜎E is neglected. We suggest a generalization by the conductive currents, i.e., when the electromagnetic field dissipates irreversibly to Joule heat. The presented procedure enables us to introduce also the Lagrangian formulation of the discussed dissipated electromagnetic waves. It paves a new way involving damping physical fields in a thermodynamic frame.

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“…There are electromagnetic problems that cannot be solved or are complicated to solve without the Hertz vector [17]. The symmetry of the Maxwell equations allow an alternative introduction of the Hertz vector involving its gauge symmetries [18][19][20]. Ornigotti et al have shown that due to the transversality of the electromagnetic wave, the Hertz vector can be expressed as a product of a constant polarization vector and a scalar potential [21].…”

Section: Introduction: Reversible Electromagnetic Fieldmentioning

confidence: 99%

Generalized Hertz vector in the dissipative electrodynamics

Gambár¹,

Márkus²

2022

Preprint

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In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method is sometimes more effective than the scalar and vector potential-based relations. Finally, the measurable field variables, the electric and magnetic fields, can be deduced by direct calculation from the Hertz vector. However, right now, the introduction of the Hertz vector operates if the conductive currents j = σE are neglected. We suggest a generalization for the case of conductive currents, i.e., for such cases when the electromagnetic field dissipates irreversibly into Joule heat. The presented procedure enables us to introduce also the Lagrangian formulation of the discussed dissipated electromagnetic waves. It opens a new way for future studies.

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Optical helicity and Hertz vectors

Cited by 5 publications

References 35 publications

Zilch vortical effect

Zilch vortical effect

Generalized Hertz Vector in the Dissipative Electrodynamics

Generalized Hertz vector in the dissipative electrodynamics

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