Octonion form of duality-invariant field equations for dyons

2022

Eur. Phys. J. Plus

The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major influencing factors relevant to the direct and inverse piezoelectric effects. J. C. Maxwell was the first to adopt the algebra of quaternions to describe the physical quantities of electromagnetic fields. The contemporary scholars utilize the quaternions and octonions to research the physical properties of electromagnetic and gravitational fields. The application of octonions is able to study the physical quantities of electromagnetic and gravitational fields, including the octonion field strength, field source, linear moment, angular moment, torque and force. When the octonion force is equal to zero, it is capable of achieving eight independent equations, including the force equilibrium equation, fluid continuity equation, current continuity equation, and second-precession equilibrium equation and others. One of inferences derived from the second-precession equilibrium equation is that the electric current and derivative of electric moments are able to excite each other. The external derivative of electric moments can induce the electric currents. Meanwhile the external electric currents are capable of inducing the derivative of electric moments. The research states that this inference can be considered as the underlying mechanism for the direct and inverse piezoelectric effects. Further the second-precession equilibrium equation is able to predict several new influencing factors of direct and inverse piezoelectric effects.

Section: Introductionmentioning

confidence: 95%

One underlying mechanism for two piezoelectric effects in the octonion spaces

2022

Eur. Phys. J. Plus

“…What the paper studies is the classical octonion, which was invented by T. Graves and A. Cayley independently. In order to study gravi-electromagnetism, 19,20 dark matter, 21 dyons, 22,23 and others, some scholars developed the nonclassical octonions, including the hyperbolic octonions, split octonions, pseudo-octonions, and Cartan's octonions. The classical octonions and the nonclassical octonions complement each other to a certain extent.…”

Section: Introductionmentioning

confidence: 99%

Torques and angular momenta of fluid elements in the octonion spaces

Math Methods in App Sciences

2022

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell was the first to introduce the quaternions to study the physical properties of electromagnetic fields.The contemporary scholars utilize the quaternions and octonions to investigate the electromagnetic theory, gravitational theory, quantum mechanics, special relativity, general relativity and curved spaces and so forth. The paper adopts the octonions to describe the electromagnetic and gravitational theories, including the octonionic field potential, field strength, linear momentum, angular momentum, torque and force and so on. In case the octonion force is equal to zero, it is able to deduce eight independent equations, including the fluid continuity equation, current continuity equation, and force equilibrium equation and so forth. Especially, one of the eight independent equations will uncover the interrelation of the external torque and angular momentums of fluid elements. One of its inferences is that the direction, magnitude and frequency of the external torque must impact the direction and curl of the angular momentum of fluid elements, altering the frequencies of Karman vortex streets within the fluids. It means that the external torque is interrelated with the velocity circulation, by means of the liquid viscosity. The external torque is able to exert an influence on the direction of downwash flows, improving the lift and drag characteristics generated by the fluids.

“…J. C. Maxwell first applied not only the algebra of quaternions but also the vector analysis to explore the physical properties of electromagnetic fields. The subsequent scholars 10 uti-lize the quaternions 11 and octonions 12 to study the electromagnetic fields 13,14 , gravitational fields 15 , invariants 16,17 , conservation laws, continuity equations, quantum mechanics 18,19 , relativity 20 , astrophysical jets, weak nuclear fields 21,22 , strong nuclear fields 23,24 , black holes 25 , and dark matters 26 and so forth.…”

Section: Introductionmentioning

confidence: 99%

Basic postulates of some coordinate transformations within material media

2022

AIP Advances

This paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws, and continuity equations, in the electromagnetic and gravitational fields. Maxwell first utilized quaternions to describe the electromagnetic theory. Subsequent scholars make use of octonions to study the physical properties of electromagnetic and gravitational fields simultaneously, including the octonion field strength, field source, angular momentum, torque, and force. When an octonion coordinate system transforms rotationally, the scalar part of one octonion will remain unchanged, although the vector part of the octonion may alter. In the octonion space [Formula: see text], some invariants can be derived from this octonion property. A part of these invariants can be selected as the basic postulates of Galilean transformation or Lorentz transformation. Similarly, several invariants can be derived from the octonion property in the transformed octonion space [Formula: see text], and the invariants can be chosen as the basic postulates of a few new types of coordinate transformations. Furthermore, the combination of invariants in the octonion spaces can be applied as the basic postulates of some new coordinate transformations, relevant to the norm of physical quantities. Through the analysis, it is easy to find that each conserved quantity has its preconditions from the perspective of octonion spaces. This is helpful to deepen the further understanding of the physical properties of conservation laws and other invariants.