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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…
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 extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe…
The paper focuses on applying the algebra of octonions to study some coordinate transformations in the octonion spaces, exploring the contribution of partial field potential on the speed of light. J. C. Maxwell was the first to introduce…
The paper aims to explore the impact of composite operators containing a few physical quantities on the gravitational and electromagnetic fields, studying the influencing factors and physical properties of octonion field equations. J. C.…
The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of…
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum…
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…
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…
The paper aims to apply the octonions to explore the torques and forces and so forth in the electromagnetic and gravitational fields, investigating the influences of material media on the equilibrium and continuity equations. 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,…
The paper aims to apply the octonions to explore the contribution of some influence factors to magnetic moments, revealing the connection among the influence factors and spin texture. J. C. Maxwell was the first to introduce the quaternions…
The paper focuses on applying the octonions to explore the electromagnetic and gravitational equations in the presence of some material media, exploring the frequencies of astrophysical jets. Maxwell was the first to use the algebra of…
The paper focuses on applying the algebra of octonions to explore the influence of electric-charge gradients on the electric-current derivatives, revealing some of major influence factors of high pulse electric-currents. J. C. Maxwell was…
There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for…
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…
The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell…
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…
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 discusses the impact of adjoint fields on the conservation laws in the gravitational field and electromagnetic field, by means of the characteristics of octonions. When the adjoint field can not be neglected, it will cause the…