Octonionic Geometry

Abstract

We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented. Eight real parameters of octonions are interpreted as the space-time coordinates, momentum and energy. In our approach the two fundamental constants, $c$ and $\hslash$, have the geometrical meaning and appear from the condition of positive definiteness of the octonion norm. We connect the property of non-associativity with the time irreversibility and fundamental probabilities in physics.

11 pages, no figures

Cited by in corpus (16)

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• Octonionic Version of Dirac Equations
• Geometrical Applications of Split Octonions
• Rotations in the Space of Split Octonions
• Colorless operators in a non-associative quantum theory
• The unifying formula for all Tribonacci-type octonions sequences and their properties
• Geometry of the Non-Compact G(2)
• A new derivation of the Minkowski metric
• A note on dual third order Jacobsthal vectors
• Algebraical Entropy and Arrow of Time
• The Third Order Jacobsthal Octonions: Some Combinatorial Properties
• Quantum of area from gravitation on complex octonions
• Nonassociative quantum theory, emergent probability, and coquasigroup symmetry
• Dirac and Maxwell systems in split octonions
• Extended Relativity: Beyond
• Split octonionic Dirac equation