Octonion Algebra
A presentation of the algebra and its connection to physics
Abstract:
This document defines the 16 possible ways to construct Octonion Algebra, and their 2
non-isomorphic groupings defined as Left and Right Octonion Algebra.
A law of Algebraic Invariance is presented. A Variance Sieve algorithm is presented to sort
out invariant and variant product terms.
Octonion Algebra is shown to match the multiplication characteristics of the standard
Electrodynamic fields, providing a suitable basis.
The Octonion Ensemble Derivative Form is presented as the foundation for Octonion
Calculus. The Ensemble Derivative applied to an 8-potential are shown to provide
candidates for the Electric, Magnetic and Gravitational fields.
The Invariant 8-current and the Invariant Action Function (work-force Octonion form) are
presented. The Law of Algebraic Invariance is used to convert the Action Function into an
integrable form. This form is presented as the divergence of the Octonion
Stress-Energy-Momentum Tensor. Its Integration produces the conservation equations for
energy and momentum.
Restriction on the Stress-Energy-Momentum Tensor to its Electrodynamics components is
shown to produce the same results as classical Electrodynamics.
Copyright 2008, Richard Lockyer
email: rick@octospace.com