Related papers: Interpretations of Octonion Wave Equations
Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively, corresponding field equation, equation of motion and…
The sedenion compounding fields and their quantum interplays can be presented by analogy with the octonionic electromagnetic, gravitational, strong and weak interactions. In sedenion fields which are associated with electromagnetic,…
In "Octonion Algebra and its Connection to Physics" [16] an algorithm on octonions is brought forward for description of physical law, the "octonion variance sieve process". This paper expresses the used algorithm in symbolic form, and…
With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
Working over the split octonions over an algebraically closed field, we solve all polynomial equations in which all the coefficients but the constant term are scalar. As a consequence, we calculate the n-th roots of an octonion.
An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the…
We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts…
The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. J. C. Maxwell was the first to utilize…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…
In the framework of Einstein-Maxwell-axion theory we consider static spherically symmetric solutions, which describe a magnetic monopole in the axionic environment. These solutions are interpreted as the solutions for an axionic dyon, the…
In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…
The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of…
We consider mathematical aspects of the axion electrodynamics in application to the problem of evolution of geomagnetic and terrestrial electric fields, which are coupled by relic axions born in the early Universe and (hypothetically)…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
We suppose that the covariance of Lagrangians always taking place results in a distortion of any electric and magnetic field by a pseudoscalar field of dark matter axions and axion-like particles. As a result, electric and magnetic fields…
The dual magneto-hydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing…