Generalized Octonion Electrodynamics

Chanyal, B. C.; Bisht, P. S.; Negi, O. P. S.

doi:10.1007/s10773-010-0314-5

Cited by 85 publications

(47 citation statements)

References 38 publications

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“…V. L. Mironov etc 12 described the electromagnetic equations and related features with the algebra of octonions. O. P. S. Negi etc 13 depicted the Maxwell's equations by means of the octonion. S. Demir 14 expressed the gravitational field equations with the octonion.…”

Section: Introductionmentioning

confidence: 99%

Angular momentum and torque described with the complex octonion

Weng

2014

AIP Advances

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The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of two fields can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential, field strength, field source, current continuity equation, and electric (or magnetic) dipolar moment etc in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features, including the torque, force, and mass continuity equation etc. The S-quaternion space is proper to depict the electromagnetic features, including the dipolar moment and current continuity equation etc. In case the field strength is weak enough, the force and the continuity equation etc can be respectively reduced to that in the classical field theory.Comment: 11 pages, minor change

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Section: Introductionmentioning

confidence: 99%

Angular momentum and torque described with the complex octonion

Weng

2014

AIP Advances

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“…In the complex octonion space, one complex octonion physical quantity is, 5) where For the complex octonion physical quantity, Z = Z g +k eg Z e , it can be rewritten as the exponential form,…”

Section: Discussionmentioning

confidence: 99%

Spin angular momentum of proton spin puzzle in complex octonion spaces

Weng

2017

Int. J. Geom. Methods Mod. Phys.

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The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. J. C. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.

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“…In order to write the quantum equations of dyons in isotropic media in terms of compact notations of octonions, let us start with the four dimensional representation of differential operator [17,18] expressed in terms of octonion units as…”

Section: Generalized Octonionic Maxwell's Equations In Isotropic Mediummentioning

confidence: 99%