Related papers: Some field equations with composite operators in o…
In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave…
The paper investigates the influences of the helicity on the gravitational mass density, the field source, the charge continuity equation, and the mass continuity equation etc in the electromagnetic field and gravitational field. By means…
The paper aims to study some invariants and conservation laws relevant to electromagnetic and gravitational fields, by means of the rotational transformations of octonion coordinate systems. The scholars utilize the octonions to analyze the…
The paper discusses some scalar invariants in the gravitational field and electromagnetic field by means of the characteristics of the quaternions. When we emphasize some definitions of quaternion physical quantities, the speed of light,…
Based on Maxwellian quaternionic electromagnetic theory, the electromagnetic interaction, gravitational interaction and their coupling influence with the dark matter field in octonionic space are discussed. The research results disclose the…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
Based on Maxwellian quaternionic electromagnetic theory, the octonionic hyper-strong field, hyper-weak field and the quantum interplays can be presented by analogy with octonionic electromagnetic, gravitational, strong and weak…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
The paper aims to consider the strength gradient force as the dynamic of astrophysical jets, explaining the movement phenomena of astrophysical jets. J. C. Maxwell applied the quaternion analysis to describe the electromagnetic theory. This…
The paper discusses the influences of velocity curl and field strength on some theorems in the electromagnetic field and gravitational field. With the characteristics of the algebra of quaternions, the theorem of linear momentum,…
The paper aims to apply the complex octonion to explore the influence of the energy gradient on the Eotvos experiment, impacting the gravitational mass in the ultra-strong magnetic fields. Until now the Eotvos experiment has never been…
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic…
We focus on the interaction of a plane gravitational wave with electromagnetic fields and we describe this interaction in the proper detector frame where, thanks to the introduction of Fermi coordinates, it is possible to refer to directly…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…