Forces in the complex octonion curved space

Abstract

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 electromagnetic theory. It inspires subsequent scholars to study the electromagnetic and gravitational theories with the complex quaternions/octonions. Furthermore Einstein was the first to depict the gravitational theory by means of tensor analysis and curved four-space-time. Nowadays some scholars investigate the electromagnetic and gravitational properties making use of the complex quaternion/octonion curved space. From the orthogonality of two complex quaternions, it is possible to define the covariant derivative of the complex quaternion curved space, describing the gravitational properties in the complex quaternion curved space. Further it is possible to define the covariant derivative of the complex octonion curved space by means of the orthogonality of two complex octonions, depicting simultaneously the electromagnetic and gravitational properties in the complex octonion curved space. The result reveals that the connection coefficient and curvature of the complex octonion curved space will exert an influence on the field strength and field source of the electromagnetic and gravitational fields, impacting the linear momentum, angular momentum, torque, energy, and force and so forth.

27 pages

References in corpus (2)

• Quaternions, Lorentz Group and the Dirac Theory
• Dynamic of astrophysical jets in the complex octonion space

Cited by in corpus (11)

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• On the quaternion transformation and field equations in curved space-time
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• Four interactions in the sedenion curved spaces
• Torques and angular momenta of fluid elements in the octonion spaces
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• Physical quantities and spatial parameters in the complex octonion curved space
• Contrastive analysis of two energy gradients in the ultra-strong magnetic fields
• Gravitational mass and energy gradient in the ultra-strong magnetic fields
• Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces
• Basic postulates of some coordinate transformations within material media