Related papers: Field Equations in the Complex Quaternion Spaces
The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major influencing factors relevant to the direct and…
Superluminal electromagnetic fields of dyons are described in T^{4}- space and Quaternion formulation of various quantum equations is derived. It is shown that on passing from subluminal to superluminal realm via quaternion the theory of…
The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and…
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 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,…
By means of the rotational transformations of octonion coordinate systems, the paper aims to explore the physical properties of conserved quantities relevant to the vectorial magnitudes within the material media, revealing the simultaneity…
The paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws and continuity equations, in the electromagnetic and…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This…
The 32-dimensional compounding fields and their quantum interplays in the trigintaduonion space can be presented by analogy with octonion and sedenion electromagnetic, gravitational, strong and weak interactions. In the trigintaduonion…
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.…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
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…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex,…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…
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…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…