Reconstruction of symmetric Dirac–Maxwell equations using nonassociative algebra

2015 ◽  
Vol 12 (03) ◽  
pp. 1550029 ◽  
Author(s):  
Pushpa Kalauni ◽  
J. C. A. Barata
Keyword(s):  
Magnetic Fields ◽  
Maxwell Equations ◽  
Matrix Representation ◽  
Single Equation ◽  
Magnetic Monopoles ◽  
Nonassociative Algebra ◽  
Compact Representation ◽  
Duality Transformation ◽  
Electric And Magnetic Fields ◽  
Algebraic Properties

In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac–Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.

scholarly journals A Model of Magnetic Monopoles

1997 ◽  
Vol 12 (40) ◽  
pp. 3153-3159 ◽  
Author(s):  
Rainer W. Kühne
Keyword(s):  
Electric Charge ◽  
Quantum Electrodynamics ◽  
Maxwell Equations ◽  
Rest Frame ◽  
Electromagnetic Interaction ◽  
Magnetic Monopoles ◽  
Relativity Principle ◽  
Electric And Magnetic Fields ◽  
Physical Effects ◽  
Field Theoretical Model

The possibility of the existence of magnetic charges is one of the greatest unsolved issues of the physics of this century. The concept of magnetic monopoles has at least two attractive features: (i) Electric and magnetic fields can be described equivalently. (ii) In contrast to quantum electrodynamics, models of monopoles are able to explain the quantization of electric charge. We suggest a quantum field theoretical model of the electromagnetic interaction that describes electricity and magnetism as equivalent as possible. This model requires the cross-section of Salam's "magnetic photon" to depend on the absolute motion of the electric charge with which it interacts. We suggest a tabletop experiment to verify this magnetic photon. Its discovery by the predicted effect would have far-reaching consequences: (i) Evidence for a new gauge boson and a new kind of radiation which may find applications in medicine. (ii) Evidence for symmetrized Maxwell equations. (iii) Evidence for an absolute rest frame that gives rise to local physical effects and violation of Einstein's relativity principle.

scholarly journals The Dual Continuity Equations

2018 ◽  
Author(s):  
Arbab Arbab ◽  
Norah N. Alsaawi
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Gauge Invariance ◽  
Maxwell Equations ◽  
Continuity Equation ◽  
Mathematical Structure ◽  
Magnetic Monopoles ◽  
System Of Equations ◽  
Duality Transformation ◽  
Continuity Equations

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

scholarly journals The New Field Quantities and the Poynting Theorem in Material Medium with Magnetic Monopoles

2016 ◽  
Vol 67 (6) ◽  
pp. 444-448
Author(s):  
Ömer Zor
Keyword(s):  
Dimensional Analysis ◽  
Lorentz Force ◽  
Constitutive Equations ◽  
Maxwell Equations ◽  
Magnetic Monopoles ◽  
Magnetic Intensity ◽  
Duality Transformation ◽  
Material Medium ◽  
Si Units ◽  
Poynting Theorem

Abstract The duality transformation was used to define the polarization mechanisms that arise from magnetic monopoles. Then, a dimensional analysis was conducted to describe the displacement and magnetic intensity vectors (constitutive equations) in SI units. Finally, symmetric Maxwell equations in a material medium with new field quantities were introduced. Hence, the Lorentz force and the Poynting theorem were defined with these new field quantities, and many possible definitions of them were constructed.

scholarly journals Field of a moving locked charge in classical electrodynamics

2020 ◽  
Vol 35 (32) ◽  
pp. 2050267
Author(s):  
Alexander J. Silenko
Keyword(s):  
Wave Function ◽  
Spatial Distribution ◽  
Magnetic Fields ◽  
Electric Field ◽  
Charge Density ◽  
Maxwell Equations ◽  
Classical Electrodynamics ◽  
Closed Space ◽  
Electric And Magnetic Fields ◽  
Average Electric Field

The paradox of a field of a moving locked charge (confined in a closed space) is considered and solved with the use of the integral Maxwell equations. While known formulas obtained for instantaneous fields of charges moving along straight and curved lines are fully correct, measurable quantities are average electric and magnetic fields of locked charges. It is shown that the average electric field of locked charges does not depend on their motion. The average electric field of protons moving in nuclei coincides with that of protons being at rest and having the same spatial distribution of the charge density. The electric field of a twisted electron is equivalent to the field of a centroid with immobile charges whose spatial distribution is defined by the wave function of the twisted electron.

scholarly journals London-Proca-Hirsch Equations for Electrodynamics of Superconductors on Cantor Sets

2015 ◽  
Vol 4 ◽  
pp. 1-7 ◽  
Author(s):  
Victor Christianto
Keyword(s):  
Magnetic Fields ◽  
Maxwell Equations ◽  
High Energy Physics ◽  
High Energy ◽  
Cantor Sets ◽  
Vector Calculus ◽  
Electric And Magnetic Fields ◽  
Proca Equations ◽  
First Time ◽  
Energy Physics

In a recent paper published at Advances in High Energy Physics (AHEP) journal, Yang Zhao et al. derived Maxwell equations on Cantor sets from the local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. However, so far there is no derivation of equations for electrodynamics of superconductor on Cantor sets. Therefore, in this paper I present for the first time a derivation of London-Proca-Hirsch equations on Cantor sets. The name of London-Proca-Hirsch is proposed because the equations were based on modifying Proca and London-Hirsch’s theory of electrodynamics of superconductor. Considering that Proca equations may be used to explain electromagnetic effects in superconductor, I suggest that the proposed London-Proca-Hirsch equations on Cantor sets can describe electromagnetic of fractal superconductors. It is hoped that this paper may stimulate further investigations and experiments in particular for fractal superconductor. It may be expected to have some impact to fractal cosmology modeling too.

scholarly journals Controlling of light with electromagnons

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
D. Szaller ◽  
A. Shuvaev ◽  
A. A. Mukhin ◽  
A. M. Kuzmenko ◽  
A. Pimenov
Keyword(s):  
Magnetic Fields ◽  
Optical Activity ◽  
Maxwell Equations ◽  
Polarization Plane ◽  
Multiferroic Materials ◽  
Transmission Coefficients ◽  
Propagation Of Light ◽  
Resonance Frequencies ◽  
Electric And Magnetic Fields ◽  
Input Radiation

Abstract Magnetoelectric coupling in multiferroic materials opens new routes to control the propagation of light. The new effects arise due to dynamic magnetoelectric susceptibility that cross-couples the electric and magnetic fields of light and modifies the solutions of Maxwell equations in media. In this paper, two major effects will be considered in detail: optical activity and asymmetric propagation. In case of optical activity the polarization plane of the input radiation rotates by an angle proportional to the magnetoelectric susceptibility. The asymmetric propagation is a counter-intuitive phenomenon and it represents different transmission coefficients for forward and backward directions. Both effects are especially strong close to resonance frequencies of electromagnons, i. e. excitations in multiferroic materials that reveal simultaneous electric and magnetic character.

A catalogue of hidden momenta

2018 ◽  
Vol 376 (2134) ◽  
pp. 20180043 ◽  
Author(s):  
David J. Griffiths
Keyword(s):  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Magnetic Monopoles ◽  
Electromagnetic Theory ◽  
Standard Variety ◽  
Theme Issue ◽  
Magnetic Dipoles ◽  
Electric And Magnetic Fields

Electromagnetic fields carry momentum: . But if the centre of energy of a (localized) system is at rest, its total momentum must be zero. The compensating term has come to be called ‘hidden’ momentum: P h  =  −  P em . It is (typically) ordinary mechanical momentum, relativistic in nature, and is ‘hidden’ only in the sense that it is not associated with motion of the system as a whole—only with that of its constituent parts. This article develops a catalogue of field momenta and hidden momenta for ideal electric and magnetic dipoles—both the ‘standard’ variety made from electric charges and currents and the ‘anomalous’ variety made from hypothetical magnetic monopoles and their currents—in the presence of electric and magnetic fields (which themselves may be produced by ‘standard’ or ‘anomalous’ sources). This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

Investigation on a field description of the chirped laser pulse

2016 ◽  
Vol 30 (06) ◽  
pp. 1650052 ◽  
Author(s):  
H. Y. Chen ◽  
S. J. Huang ◽  
Q. Song ◽  
P. X. Wang
Keyword(s):  
Magnetic Fields ◽  
Laser Pulse ◽  
Relative Frequency ◽  
Maxwell Equations ◽  
Laser Pulses ◽  
Relative Deviation ◽  
First Order ◽  
Electric And Magnetic Fields ◽  
Laser Simulations ◽  
Chirped Laser Pulse

Starting from a first-order approximate field description function for laser pulses, the method currently used to approximate chirped laser pulse (CLP) substitutes frequency and wave vector related variables with spatiotemporally varying functions. We investigated the error involved by calculating the relative deviation from Maxwell equations. Errors for the electric and magnetic fields are analyzed separately, and behaviors related to parameter changes (that is, in laser width, pulse duration and chirp parameter) were studied. Results show that aberration associated with currently used field-description functions for CLP increases monotonically with chirp parameter, and the deviation introduced by chirping is proportional to the relative frequency span of the laser. Simulations based on these functions will lead to considerable error, especially for laser pulses with large chirping.

scholarly journals ELECTROMAGNETIC FIELDS ON FRACTALS

2006 ◽  
Vol 21 (20) ◽  
pp. 1587-1600 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Magnetic Fields ◽  
Euclidean Space ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Fractional Integrals ◽  
Hausdorff Dimensions ◽  
Specific Medium ◽  
Electric And Magnetic Fields

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the integral Maxwell equations. The fractional integrals are considered as approximations of integrals on fractals. We prove that fractal can be described as a specific medium.

scholarly journals Singularities in the flying electromagnetic doughnuts

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1379-1385 ◽  
Author(s):  
Apostolos Zdagkas ◽  
Nikitas Papasimakis ◽  
Vassili Savinov ◽  
Mark R. Dennis ◽  
Nikolay I. Zheludev
Keyword(s):  
Magnetic Fields ◽  
Topological Structure ◽  
Maxwell Equations ◽  
Poynting Vector ◽  
Saddle Points ◽  
Space Time ◽  
Cycle Space ◽  
Single Cycle ◽  
Spherical Shells ◽  
Electric And Magnetic Fields

AbstractFlying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of planes, spherical shells and rings, and display a number of point singularities including saddle points and vortices. Moreover, the instantaneous Poynting vector of the field exhibits a large number of singularities, which are often accompanied by extended areas energy backflow.

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