Abstract
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.
Highlights
The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, were first proposed by Julian Schwinger as a phenomenological alternative to quarks [1, 2]
In order to obtain the octonionic equations for dyons, the complex octonionic differential operator and its conjugate should be defined in Cayley–Dickson notation as
The duality-invariant equalities were studied by Coceal et al and a different perspective was presented for physical science
Summary
The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, were first proposed by Julian Schwinger as a phenomenological alternative to quarks [1, 2]. Mathematics, physics, and many physical applications are performed by using vector, matrix, and tensor algebra In addition to these algebraic structures, the solutions and representations of physical problems are discussed with quaternions, octonions, sedenions, octons, and sedeons, which are multicomponent number systems. These algebras offer important and alternative notations of physical systems for representing them in a more compact, effective, and elegant way. The purpose of this study is to identify the duality-invariant field equations and energy conservation law for dyons in octonionic algebra representation.
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