Forces in the complex octonion curved space

Weng, Zihua

doi:10.1142/s0219887816500766

Cited by 25 publications

(23 citation statements)

References 28 publications

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“…It should be noted that these new physical quantities are different from the physical quantities in Ref. [51].…”

Section: Coupling Termmentioning

confidence: 74%

Physical quantities and spatial parameters in the complex octonion curved space

Weng

2016

Gen Relativ Gravit

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The paper focuses on finding out several physical quantities to exert an influence on the spatial parameters of complex-octonion curved space, including the metric coefficient, connection coefficient, and curvature tensor. In the flat space described with the complex octonions, the radius vector is combined with the integrating function of field potential to become a composite radius vector. And the latter can be considered as the radius vector in a flat composite-space (a function space). Further it is able to deduce some formulae between the physical quantity and spatial parameter, in the complex-octonion curved composite-space. Under the condition of weak field approximation, these formulae infer a few results accordant with the General Theory of Relativity. The study reveals that it is capable of ascertaining which physical quantities are able to result in the warping of space, in terms of the curved composite-space described with the complex octonions. Moreover, the method may be expanded into some curved function spaces, seeking out more possible physical quantities to impact the bending degree of curved spaces.

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“…It should be noted that these new physical quantities are different from the physical quantities in Ref. [51].…”

Section: Coupling Termmentioning

confidence: 74%

Physical quantities and spatial parameters in the complex octonion curved space

Weng

2016

Gen Relativ Gravit

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“…According to three postulates of the octonion field theory (see Ref. [20]), the space extended from either the electromagnetic field or gravitational field is the quaternion space. Moreover, the quaternion space H e for the electromagnetic field is independent to the quaternion space H g for the gravitational field.…”

Section: Force and Energymentioning

confidence: 99%

“…Next, the octonion angular momentum, L , is defined from the octonion linear momentum P , octonion radius vector, R = R g + k eg R e , and octonion integrating function of field potential X (see Ref. [20] ). Further, the octonion angular momentum L can be separated into,…”

Section: Angular Momentummentioning

confidence: 99%

Contrastive analysis of two energy gradients in the ultra-strong magnetic fields

Weng

2018

Int. J. Mod. Phys. A

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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 quaternions to study the physical properties of electromagnetic fields. Some scholars follow up this method in the field theories. Nowadays, they employ the complex-octonions to analyze simultaneously the physical quantities of electromagnetic and gravitational fields, including the field potential, field strength, field source, linear momentum, angular momentum, torque, and force. When the octonion force is equal to zero, it is able to deduce eight independent equilibrium equations, especially the force equilibrium equation, precession equilibrium equation, mass continuity equation, and current continuity equation. In the force equilibrium equation, the gravitational mass is variable. The gravitational mass is the sum of the inertial mass and a few tiny terms. These tiny terms will be varied with not only the fluctuation of field strength and of potential energy, but also the spatial dimension of velocity. The study reveals that it is comparatively untoward to attempt to measure directly the variation of these tiny terms of gravitational mass in the ultra-strong magnetic field. However it is not such difficult to measure the energy gradient relevant to the variation of these tiny terms of gravitational mass. In the complex-octonion space, the gravitational mass is a sort of variable physical quantity, rather than an intrinsic property of any physical object. And this inference is accordant with the academic thought of 'the mass is not an intrinsic property any more' in the unified electro-weak theory.

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“…On the basis of the basic postulates (see Ref. [63]), the complex-sedenion space is able to describe the four sorts of fundamental fields simultaneously. However, according to the electroweak theory, the four fundamental fields in the paper include the gravitational field, electromagnetic field, and strong-nuclear field, except for the existing weak-nuclear field.…”

Section: Sedenion Spacementioning

confidence: 99%

“…a) Four fundamental fields. According to the basic postulates [63], one fundamental field extends its individual space. Each of fundamental fields can be described independently by one complex-quaternion space.…”

Section: Introductionmentioning

confidence: 99%

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

Weng¹

2017

Advances in Mathematical Physics

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The paper aims to apply the complex-sedenions to explore the wavefunctions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wavefunctions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the physical properties of electromagnetic fields. His method inspires some subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, nuclear field, quantum mechanics, and gauge field. The application of complex-sedenions is capable of depicting not only the field equations of the classical mechanics on the macroscopic scale, but also the field equations of the quantum mechanics on the microscopic scale. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wavefunction, the wavefunction in the complex-quaternion space possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wavefunction is equivalent to three conventional wavefunctions with the complex-numbers. It means that the three spatial dimensions of unit vector in the complex-quaternion wavefunction can be considered as the 'three colors', naturally the color confinement will be effective. In other words, in the complex-quaternion space, the 'three colors' are only the spatial dimensions, rather than any property of physical substance. The existing 'three colors' can be merged into the wavefunction, described with the complex-quaternions.other existing theories are still unable to account for the color confinement, laying themselves open to suspicion. The assumption of color charge in the QCD is appealing for more validation experiments. Up to now, the QCD may not be really perfect yet, especially its fundamental assumption. c) Dark matter. The existence of the physical phenomena connected with the dark matters was firstly validated in the astronomy, and then was accepted generally by the whole academic circle. Nevertheless the Standard Model is blind to the existence of dark matters, and it is unable to elucidate the relevant physical phenomena either. Further the Standard Model and even the 'Beyond the Standard Model' are incapable of predicting or inferring the confirmed dark matters. It means that the research scope, in the mainstream of current unification theories, is restricted and insufficient enough. For the unification theory, which is unable to explore the dark matter, there may be still something left to be improved. Apparently an appropriate unification theory must be capable of comprising and exploring the ordinary matter and dark matter simultaneously.Presenting a striking contrast to the above is that it is able to account for a few problems, derived from the QCD and other existing theories, in the quantum mechanics described with the complex-sedenions, trying to improve the unificat...

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Forces in the complex octonion curved space

Cited by 25 publications

References 28 publications

Physical quantities and spatial parameters in the complex octonion curved space

Physical quantities and spatial parameters in the complex octonion curved space

Contrastive analysis of two energy gradients in the ultra-strong magnetic fields

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

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