Torques and angular momenta of fluid elements in the octonion spaces

Weng, Zihua

doi:10.1002/mma.8868

Cited by 3 publications

(2 citation statements)

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“…In the electromagnetic and gravitational theories described by the octonions, the quaternion operator ◊ and the field strength of two fundamental fields (electromagnetic field and gravitational field) can be combined together to form a composite operator, ◊( , ) . This has been discussed in some papers 17,18 . Subsequently, this viewpoint can be further promoted.…”

Section: Electromagnetic and Gravitational Fieldsmentioning

confidence: 96%

“…In case ℕ = 0 under certain conditions, it is able to achieve thirty-two continuity equations and equilibrium equations independent of each other, including the fluid continuity equation, current continuity equation, force equilibrium equation, torque continuity equation (see Ref. [17]), second-torque continuity equation (see Ref. [18]), second-force equilibrium equation (see Ref.…”

Section: Gauge Fieldsmentioning

confidence: 99%

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Gauge fields and four interactions in the trigintaduonion spaces

Weng

2024

Preprint

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The paper aims to apply the trigintaduonion spaces to explore the physical properties of four interactions simultaneously, including the electromagnetic fields, gravitational fields, weak nuclear fields, and strong nuclear fields. J. C. Maxwell first applied the algebra of quaternions to study the physical properties of electromagnetic fields. It inspired some subsequent scholars to introduce the quaternions, octonions, sedenions, and trigintaduonions to research the electromagnetic fields, gravitational fields, weak nuclear fields, strong nuclear fields, quantum mechanics, gauge fields, and curved spaces and so forth. The algebra of trigintaduonions is able to discuss the physical quantities of four interactions, including the field potential, field strong, field source, linear momentum, angular momentum, torque, and force. In the field theories described with the algebra of trigintaduonions, the weak nuclear field is composed of three types of fundamental fields. These three fundamental fields, related to weak nuclear fields, can describe the physical properties of weak nuclear fields collectively. This is consistent with the conclusion of the electroweak theory. Meanwhile the strong nuclear field consists of three types of fundamental fields. These three fundamental fields relevant to strong nuclear fields may investigate the physical properties of strong nuclear fields mutually. It is coincident with the deduction of quark theory. According to the properties of trigintaduonions, one can deduce the Yang-Mills equation related to the gauge fields. It means that the electromagnetic field occupies a quaternion space. The gravitational field owns one different quaternion space. The weak nuclear fields occupy three mutually independent quaternion spaces. The properties of weak nuclear fields are different from those of electromagnetic fields or gravitational fields. According to the multiplicative closure, the strong nuclear fields also own three quaternion spaces independent of each other. These explorations further deepen the understanding of the physical properties of weak and strong nuclear fields.

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Section: Electromagnetic and Gravitational Fieldsmentioning

confidence: 96%

Section: Gauge Fieldsmentioning

confidence: 99%

Gauge fields and four interactions in the trigintaduonion spaces

Weng

2024

Preprint

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Some spin textures relevant to magnetic moments in the octonion spaces

Weng

2023

AIP Advances

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The paper aims to apply the octonions to explore the contribution of some influence factors to magnetic moments, revealing the connection between the influence factors and spin texture. Maxwell was the first to introduce the quaternions to describe the electromagnetic theory. The subsequent scholars utilized the quaternions and octonions to study the gravitational and electromagnetic theories, and so forth. The paper adopts the octonions to research the gravitational and electromagnetic fields, including the octonion’s angular momentum, torque, force, and so on. When the octonion force is equal to zero under some circumstances, it is able to achieve eight equations independent of each other. In particular, one of eight independent equations reveals the interrelation between the second-torque and the divergence of magnetic moments. One of its deductions is that the directions, magnitudes, and frequencies of some terms are capable of impacting the orientation and vortex of magnetic moments, altering the frequency of magnetic vortex clusters. It means that the spin textures are relevant to some external influence factors. Some terms may have an influence on the arrangements of spin textures. The study will be helpful for understanding the physical properties of magnetic skyrmions and merons.

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