Utilization of Riemann-Silberstein Vectors in Electromagnetics

Belkovich, Igor V.; Kogan, B. L.

doi:10.2528/pierb16051809

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…In this section, we propose TF formulation of electrodynamics based on the RS vector. Our FO approach is consistent with the RS vector formulation of classical electrodynamics proposed in [25,29].…”

Section: Rs Vectorsupporting

confidence: 69%

“…Our definition of the RS vector is consistent with the definition applied in engineering [29,30], where the E, H vectors are usually employed to describe electromagnetic systems (e.g., antennas and waveguides). In order to write Maxwell's equations for the RS vector F, we need to introduce an additional notation.…”

Section: Rs Vectormentioning

confidence: 87%

“…In [25][26][27][28], it is demonstrated that the RS vector provides a uniform and elegant description of electromagnetism, which connects classical and quantum electrodynamics. In [29,30], it is demonstrated that the RS vector is useful for the analysis of antenna and propagation problems in engineering.…”

Section: Introductionmentioning

confidence: 99%

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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Stefański

Gulgowski

2021

Entropy

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In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

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Section: Rs Vectorsupporting

confidence: 69%

Section: Rs Vectormentioning

confidence: 87%

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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Stefański

Gulgowski

2021

Entropy

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“…Representing the Maxwell equations in a matrix form, or essentially in a Dirac-like form, mostly for vacuum, has a long history [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] (see, for example, [11,12] for a comprehensive guide to the literature on the topic). These matrix representations are usually six dimensional.…”

Section: Introductionmentioning

confidence: 99%

A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium

Khan¹,

Jagannathan²

2022

Preprint

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An eight dimensional matrix representation of the Maxwell equations for a linear inhomogeneous medium has been obtained earlier based on the Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A new eight dimensional matrix representation, related to the ealier one by a similarity transformation, is derived starting ab initio from the Maxwell equations. The new representation has a more advantageous structure compared to the earlier one from the point of view of applications. In the case of a homogeneous medium the new matrix representation reduces to a block diagonal form with four two dimensional Pauli matrix blocks along the diagonal. This matrix representation of the Maxwell equations should be suitable for studying the propagation of electromagnetic waves in a linear inhomogeneous medium, particularly adopting techniques used for studying time evolution equations in quantum mechanics.

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“…The Riemann-Silberstein (RS) vector is defined as the complex sum of the electric and magnetic field vectors: E + iB. It appeared in 1907 in an article by Silberstein [1], and was applied many years later by various authors to different problems [2,3,4] (see, in particular, Ref. [3] for a historical account and full bibliography).…”

Section: Introductionmentioning

confidence: 99%

The Riemann-Silberstein vector in the Dirac algebra

Hacyan

2018

Rev. Mex. Fís.

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It is shown that the Riemann-Silberstein vector, defined as E + iB, appears naturally in the SL(2, C) algebraic representation of the electromagnetic field. Accordingly, a compact form of the Maxwell equations is obtained in terms of Dirac matrices, in combination with the null-tetrad formulation of general relativity. The formalism is fully covariant; an explicit form of the covariant derivatives is presented in terms of the Fock coefficients.

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Utilization of Riemann-Silberstein Vectors in Electromagnetics

Cited by 8 publications

References 11 publications

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium

The Riemann-Silberstein vector in the Dirac algebra

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