This website is a repository for papers I have written describing my research into the

application of Octonion Algebra to Physics. Understanding the application requires an

understanding of Octonion Algebra itself. There are perspectives on the algebra that

anyone interested in Octonions for any reason may find enlightening, and will not be able

to find anywhere else for now.

**Highlights of original work**

There are only two truly different multiplication tables for Octonion Algebra, not 480.

They can be classified as Left Octonion or Right Octonion. For a given set of 7

permutation triplets, there are only 8 Right and 8 Left Octonion Algebras, not 128.

Creation methods for all possible valid Octonion Algebras and mappings between them.

The Law of Octonion Algebraic Invariance, and the Octonion Variance Sieve Process.

The Octonion Ensemble Derivative Form as the foundation for Octonion Calculus.

The Invariant 8-current and the Invariant Action Function (work-force Octonion form).

Applying the Law of Algebraic Invariance to convert the Action Function to an equivalent

integrable form. Equating the Action Function to its integrated form to produce the

Octonion Conservation of Energy and Momentum Equations. Electrodynamics is fully

covered as a subset of the presentation.

application of Octonion Algebra to Physics. Understanding the application requires an

understanding of Octonion Algebra itself. There are perspectives on the algebra that

anyone interested in Octonions for any reason may find enlightening, and will not be able

to find anywhere else for now.

They can be classified as Left Octonion or Right Octonion. For a given set of 7

permutation triplets, there are only 8 Right and 8 Left Octonion Algebras, not 128.

Creation methods for all possible valid Octonion Algebras and mappings between them.

The Law of Octonion Algebraic Invariance, and the Octonion Variance Sieve Process.

The Octonion Ensemble Derivative Form as the foundation for Octonion Calculus.

The Invariant 8-current and the Invariant Action Function (work-force Octonion form).

Applying the Law of Algebraic Invariance to convert the Action Function to an equivalent

integrable form. Equating the Action Function to its integrated form to produce the

Octonion Conservation of Energy and Momentum Equations. Electrodynamics is fully

covered as a subset of the presentation.

Copyright 2008-2010 Richard Lockyer

email: rick@octospace.com

Hadamard Matrix Connection to the Octonions

Quaternion Doubling for all Octonion Algebras

Octonion Torque Variances

16 Octonion Algebras - 480 Representations

Quaternion Doubling for all Octonion Algebras

Octonion Torque Variances

16 Octonion Algebras - 480 Representations

Somewhat new

Somewhat new

Somewhat New

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Somewhat new

Somewhat New

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