Some properties of dark matter field in the complex octonion space

Weng, Zihua

doi:10.1142/s0217751x15502127

Cited by 19 publications

(7 citation statements)

References 61 publications

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“…A 0 = A 0 D 0 , and A = Σ A k D k . The selection of coordinate axes [37] in the quaternion space H e is similar to that in the quaternion space H g .…”

Section: Octonion Field Sourcementioning

confidence: 99%

Superconducting currents and charge gradients in the octonion spaces

Weng

2020

Preprint

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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 the first scholar to utilize the algebra of quaternions to study the physical properties of electromagnetic fields. The contemporary scholars employ simultaneously the quaternions and octonions to investigate the physical properties of electromagnetic fields, including the octonion field strength, field source, linear momentum, angular momentum, torque, and force and so forth. When the octonion force is equal to zero, it is able to achieve eight equations independent of each other, including the fluid continuity equation, current continuity equation, force equilibrium equation, and second-force equilibrium equation and so on. One of inferences derived from the second-force equilibrium equation is that the charge gradient and current derivative are interrelated closely, two of them must satisfy the need of the second-force equilibrium equation synchronously. Meanwhile the electromagnetic strength and linear momentum both may exert an influence on the current derivative to a certain extent. The above states that the charge gradient and current derivative are two correlative physical quantities, they must meet the requirement of second-force equilibrium equation. By means of controlling the charge gradients and other physical quantities, it is capable of restricting the development process of current derivatives, reducing the damage caused by the instantaneous impact of high pulse electric-currents, enhancing the anti-interference ability of electronic equipments to resist the high pulse electric-currents and their current derivatives. Further the second-force equilibrium equation is able to explain two types of superconducting currents.

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“…A 0 = A 0 D 0 , and A = Σ A k D k . The selection of coordinate axes [37] in the quaternion space H e is similar to that in the quaternion space H g .…”

Section: Octonion Field Sourcementioning

confidence: 99%

Superconducting currents and charge gradients in the octonion spaces

Weng

2020

Preprint

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“…Further, in the complex-octonion space O , for the classical electromagnetic field on the macroscopic scale, it is capable of deducing the definitions of the electromagnetic strength and electromagnetic source (see Ref. [18]), from the field equations, ♦ g • A e = F e , and ♦ * g • F e = −µS e , respectively. Similarly, in the complex-octonion space O , for the electromagnetic quantum-field on the microscopic scale, there may be one comparatively simple situation that the contribution of term, {iZ W • W ⋆ /( v 0 )} can be neglected approximately.…”

Section: B Space Transformationmentioning

confidence: 99%

“…And it inspired the subsequent scholars to apply the quaternions, octonions, and sedenions to investigate the gravitational field, electromagnetic field, nuclear field, Dirac wave equation, Yang-Mills equation, electroweak field, color confinement, and dark matter field and so forth. When a part of coordinate values are complex-numbers, the quaternion, octonion, and sedenion are called as the complex-quaternion, complex-octonion, and complex-sedenion respectively.In recent years, a part of scholars make use of the algebra of quaternions to research the electromagnetic field equations, quantum mechanics, gravitational fields, dark matters [18], and curved space and so on. Edmonds [19] expressed the wave equation and gravitational theory with the quaternion in the curved spacetime.…”

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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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“…J. C. Maxwell was the first to apply the quaternions to explore the properties of electromagnetic fields. Presently, some scholars utilize the quaternions [26,27], octonions [28,29,30], and sedenions [31,32,33] to research the gravitational field equations [34,35], electromagnetic field equations [36], Dirac wave equations, Yang-Mills equations, curved space [37], astrophysical jet, and dark matter [38,39,40] and so forth.…”

Section: Introductionmentioning

confidence: 99%

Four interactions in the sedenion curved spaces

Weng

2018

Preprint

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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 complexsedenions, 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'.

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Some properties of dark matter field in the complex octonion space

Cited by 19 publications

References 61 publications

Superconducting currents and charge gradients in the octonion spaces

Superconducting currents and charge gradients in the octonion spaces

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

Four interactions in the sedenion curved spaces

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