Octonionic Electrodynamics

Abstract

Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic monopoles in classical electrodynamics is connected with the using of associativity limit.

The version accepted by J. Phys. A

Cited by in corpus (45)

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• Octonic Electrodynamics
• Generalized Split-Octonion Electrodynamics
• Split Quaternions and Particles in (2+1)-Space
• Forces in the complex octonion curved space
• Unified Split Octonion Formulation of Dyons
• Field Equations in the Complex Quaternion Spaces
• Some properties of dark matter field in the complex octonion space
• Geometrical Applications of Split Octonions
• Quaternionic electrodynamics
• Rotations in the Space of Split Octonions
• Dynamic of astrophysical jets in the complex octonion space
• Third-order Jacobsthal Generalized Quaternions
• Angular momentum and torque described with the complex octonion
• Torques and angular momenta of fluid elements in the octonion spaces
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• Toy models of a non-associative quantum mechanics
• Some spin textures relevant to magnetic moments in the octonion spaces
• Contrastive analysis of two energy gradients in the ultra-strong magnetic fields
• A Remarkable New Identity Satisfied by the Dirac Matrices of a Bilocal Field Theory
• Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics
• The unifying formula for all Tribonacci-type octonions sequences and their properties
• On a class of gauge theories
• Geometry of the Non-Compact G(2)
• Gravitational mass and energy gradient in the ultra-strong magnetic fields
• Algebraical Entropy and Arrow of Time
• A note on dual third order Jacobsthal vectors
• The Third Order Jacobsthal Octonions: Some Combinatorial Properties
• Hamilton's equations in a non-associative quantum theory
• Quantum of area from gravitation on complex octonions
• Nonassociative quantum theory, emergent probability, and coquasigroup symmetry
• Nonassociatuve generalization of supersymmetry
• Field equations of electromagnetic and gravitational fields
• Dirac and Maxwell systems in split octonions
• Frequencies of astrophysical jets and gravitational strengths in the octonion spaces
• Hidden structures in quantum mechanics
• Sedeonic theory of massless fields
• Remarks on four dimensional Euclidean gravity without Wick rotation
• Extended Relativity: Beyond
• Crystallography, relativity and octonions
• Some Wave Equations for Electromagnetism and Gravitation
• The simplest non-associative generalization of supersymmetry
• Octonionic formulation of the fully symmetric Maxwell's equations in 3+1 dimensions
• An analysis of Rick Lockyer's "octonion variance sieve"
• Split octonionic Dirac equation