Four interactions in the sedenion curved spaces

Abstract

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 quaternions to describe the property of electromagnetic fields. Nowadays the scholars introduce the complex-octonions to depict the electromagnetic and gravitational fields. And the complex-sedenions can be applied to study the field equations of the four interactions in the classical mechanics and quantum mechanics. Further, it is able to extend the field equations from the flat space into the curved space described with the complex-sedenions, by means of the tangent-frames and tensors. The research states that a few physical quantities will make a contribution to certain spatial parameters of the curved spaces. These spatial parameters may exert an influence on some operators (such as, divergence, gradient, and curl), impacting the field equations in the curved spaces, especially the field equations of the four quantum-fields in the quantum mechanics. Apparently the paper and General Relativity both confirm and succeed to the Cartesian academic thought of `the space is the extension of substance'.

International Journal of Geometric Methods in Modern Physics. 2018, 12. arXiv admin note: text overlap with arXiv:1611.01019

References in corpus (10)

• Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Forces in the complex octonion curved space
• Some properties of dark matter field in the complex octonion space
• Cosmological aspects of a unified dark energy and dust dark matter model
• A cosmotopological relation for a unified field theory
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• Physical quantities and spatial parameters in the complex octonion curved space
• Domain walls and fermion scattering in Grand Unified models
• Combining gravity with the forces of the standard model on a cosmological scale

Cited by in corpus (1)

• On the quaternion transformation and field equations in curved space-time