Related papers: Some field equations with composite operators in o…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
The magneto-optic effects and electro-optic effects are the essential optic effects, although their theoretical explanations are not unified in the classical electromagnetic theory. Describing with the algebra of octonions, the…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
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…
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…
It is shown that relative coordinate and momentum of coherent electron pair have the meaning of observables with the help of quadrupole and magnetic moments. Distributions of quadrupole terms of scalar potential are shown. These…
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…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
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…
Magnetic properties of octet baryons are investigated within the framework of chiral perturbation theory. Utilizing a power counting for large magnetic fields, the Landau levels of charged mesons are treated exactly giving rise to baryon…
We use a quantum mechanical charged particle as a test particle which probes the dynamics of force-related fields it is subject to. We allow for geodesic motion and relations involving gravitation appear. Gravitation affects quantum…
Demonstrating the split octonion formalism for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), relevant field equations are derived in compact, simpler and manifestly…
Based on the electromagnetic interaction and gravitational interaction, the quantum interplays of the ordinary matter and the dark matter in the octonion space are discussed. The paper presents the quantization of the particles of ordinary…
We present a calculation of the electric and magnetic form factors of ground-state octet and decuplet baryons including strange quarks. We work with a combination of Dyson-Schwinger equations for the quark propagator and covariant…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…
In the presence of an electromagnetic (EM) field the space-time metrics are affected by the field potential. The principle of superposition, which usually rules EM fields, is no longer valid for the biggest fields and Maxwell's equations,…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
Making use of the octonion operator, the electromagnetic field generates an adjoint field theoretically. The source of adjoint field includes the adjoint charge and the adjoint current. The adjoint charge has an impact on the gravitational…
Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…