Authors: Cohl Furey
Publish Date: 2014/10/07
Volume: 2014, Issue: 10, Pages: 46-
Abstract
We point out a somewhat mysterious appearance of SUc3 representations which exhibit the behaviour of three full generations of standard model particles These representations are found in the Clifford algebra ℂl6 arising from the complex octonions In this paper we explain how this 64complexdimensional space comes about With the algebra in place we then identify generators of SU3 within it These SU3 generators then act to partition the remaining part of the 64dimensional Clifford algebra into six triplets six singlets and their antiparticles That is the algebra mirrors the chromodynamic structure of exactly three generations of the standard model’s fermions Passing from particle to antiparticle or vice versa requires nothing more than effecting the complex conjugate ∗ i ↦ − i The entire result is achieved using only the eightdimensional complex octonions as a single ingredientThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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