On a Quaternionic Reformulation of Maxwell's Equations for Chiral Media and its Applications

Kravchenko, Vladislav V.; Oviedo, Hector

doi:10.4171/zaa/1163

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…In the present work (section 4) we show that in a very important for applications case of α being a function of one Cartesian variable a particular solution of (3) is always available in a simple explicit form. This situation corresponds to models describing waves propagating in stratified media (see, e.g., [16]). As a result in this case we are able to construct a complete system of solutions explicitly which for many purposes means a general solution.…”

Section: Introductionmentioning

confidence: 95%

On Beltrami fields with nonconstant proportionality factor on the plane

Kravchenko

Oviedo

2008

Reports on Mathematical Physics

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Section: Introductionmentioning

confidence: 95%

On Beltrami fields with nonconstant proportionality factor on the plane

Kravchenko

Oviedo

2008

Reports on Mathematical Physics

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“…The first case corresponds to the Maxwell equations and the second to the Dirac equation (see [4,8]). Following [8,14,15], but by considering the chiral representation, the Dirac equation in its covariant form…”

Section: The Dirac Equation In Quaternionic Formmentioning

confidence: 99%

“…The difference between this c  and  of [8,14,15] is that here the Dirac Equation (2) is in the Weyl or chiral representation. This equality shows that instead of Equation (2) we can consider the equivalent quaternionic equation…”

Section: The Dirac Equation In Quaternionic Formmentioning

confidence: 99%

Chiral Dirac Equation Derived From Quaternionic Maxwell’s Systems

Torres-Silva¹

2013

JEMAA

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In the present article, we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg's measurement-disturbation relationship and mass generation in systems like graphene devices.

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“…(see i.e. [8], [12]), and because of that, new exact solutions can be obtained for some classes of [12], [13], [14]. Notice also that this approach does not need to be twicecontinuously differentiable, but only once, which includes a wider class of physical cases.…”

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confidence: 99%

On the advances of two and three-dimensional electrical impedance equation

Tachiquin

Nava

Jaso

et al. 2008

2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control

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We review the state of the art of solutions for the electrical impedance equation div( grad ') = 0;(1)where the function = + i!" is the admitivity, denotes the conductivity, ! is the frequency, " is the permittivity, i is the imaginary unit, and ' denotes the electric potential. Considering the three-dimensional case, we show that this equation is equivalent to a Schrödinger equation, and applying the algebra of quaternions, we study one method for factorizing (1) into two rst-order differential operators. We also discuss a method for rewriting equation (1) directly into a quaternionic rst-order linear differential equation and we cite some cases when it is possible to solve it analytically. For the two-dimensional case, we show that (1) is equivalent to a Vekua equation, and applying recently discovered properties of pseudoanalytic functions, we explore how to obtain solutions of (1) starting with solutions of a two-dimensional Schrödinger equation. Once we have discussed some elements of Pseudoanalytic Function Theory, we expose how to express the general solution of the Electrical Impedance Equation through Taylor series in formal powers, remarking the impact of this tools in such important questions as the Calderon problem in the plane.

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On a Quaternionic Reformulation of Maxwell's Equations for Chiral Media and its Applications

Cited by 12 publications

References 17 publications

On Beltrami fields with nonconstant proportionality factor on the plane

On Beltrami fields with nonconstant proportionality factor on the plane

Chiral Dirac Equation Derived From Quaternionic Maxwell’s Systems

On the advances of two and three-dimensional electrical impedance equation

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