A new approach on electromagnetism with dual number coefficient octonion algebra

The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, are widely discussed in application to electromagnetic theory and magnetohydrodynamics. Particularly, the duality-invariant field equations were suggested with suitable definitions of the dyon's electromagnetic characteristics. In this study, we propose an alternative formulation of the duality-invariant field equations for dyons based on octonion algebra. Octonions have been used to express the equations for potentials, field strengths, and sources in a more compact and consistent manner.Additionally, the octonionic form of the energy conservation law for dyons has been derived.

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“…Using divergence, curl, and time derivative expressions of (21) and (22), expression (45) can be represented in a simple form:…”

Section: Duality-invariant Field Equations In Octonion Formmentioning

confidence: 99%

Octonion form of duality-invariant field equations for dyons

Kansu¹,

Tanışlı²,

Demir³

2020

Turk J Phys

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“…where V ¡ (A + iB) and � ¡ �� e � i� m � are vector and scalar potentials of the dyon [22]. Moreover, the classical field equations of dyons and its conservation laws have already been discussed [23][24][25][26][27]. From (80), we get the following changes in differential operators:…”

Section: Quantum Wave Propagation In An External Electromagnetic Fiel...mentioning

confidence: 99%

A relativistic quantum theory of dyons wave propagation

Chanyal

2017

Can. J. Phys.

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Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).Comment: 8 pages. arXiv admin note: text overlap with arXiv:hep-th/0608164 by other author

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“…However, the Clifford-octonion algebra is an extension of the octonion algebra, having a sixteen-dimensional structure with dual unity that helps to study unified theories in physics. In order to study the dual-octonionic formalism for the electromagnetic field of dyons and keeping in mind the recent work on the dual octonion algebra [14][15][16], let us start with the following dual form of real numbers,…”

Section: Clifford-octonion Algebramentioning

confidence: 99%

“…Now, we can apply the dual-octonionic function to the electromagnetism of dyons. If we concern the classical electrodynamics of dyons (having both electric and magnetic charges) in the four-dimensional spacetime world, the differential operator , which has four-dimensional Euclidean space-time components, can be governed as (11) and the dual-octonion potential of dyons [14]…”

Section: Clifford-octonionic Maxwell Equationsmentioning

confidence: 99%

A Complete Set of Conservation Laws of Dyons with the Clifford-Octonion Algebra

Chanyal

2017

Ukr. J. Phys.

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The Clifford-octonion algebra is the highest hypercomplex algebra over a real field with Clifford coefficient (). The paper aims to apply the Clifford-octonion algebra (or simply called dualoctonion algebra) to describe the consistence theory of generalized electromagnetism and its conservation laws for dyons. The present paper describes the property of Lorentz invariance symmetries of dyons and their corresponding conservation laws. Moreover, we have studied the conservation of mass-energy, liner momentum, and angular momentum for four-dimensional particle dyons with the Clifford-octonion algebra. In generalized Clifford-octonion electromagnetic fields, we express the work-energy theorem and the linear momentum conservation theorem corresponding to the scalar and vector components of dyons, respectively. Finally, we have constructed the dual octonion form of the angular momentum conservation law, which represents an analog of the virial theorem in mechanics.

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A new approach on electromagnetism with dual number coefficient octonion algebra

Cited by 17 publications

References 26 publications

Octonion form of duality-invariant field equations for dyons

Octonion form of duality-invariant field equations for dyons

A relativistic quantum theory of dyons wave propagation

A Complete Set of Conservation Laws of Dyons with the Clifford-Octonion Algebra

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