Generations: three prints, in colour

Furey, Cohl

doi:10.1007/JHEP10(2014)046

Open Access
Published: 07 October 2014

Generations: three prints, in colour

Cohl Furey^1,2

Journal of High Energy Physics volume 2014, Article number: 46 (2014) Cite this article

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Abstract

We point out a somewhat mysterious appearance of SU_c(3) representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found in the Clifford algebra ℂl(6), arising from the complex octonions. In this paper, we explain how this 64-complex-dimensional space comes about. With the algebra in place, we then identify generators of SU(3) within it. These SU(3) generators then act to partition the remaining part of the 64-dimensional 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 eight-dimensional complex octonions as a single ingredient.

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Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
Cohl Furey
University of Waterloo, Ontario, N2L 3G1, Canada
Cohl Furey

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ArXiv ePrint: 1405.4601

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Furey, C. Generations: three prints, in colour. J. High Energ. Phys. 2014, 46 (2014). https://doi.org/10.1007/JHEP10(2014)046

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Received: 02 June 2014
Revised: 22 August 2014
Accepted: 18 September 2014
Published: 07 October 2014
DOI: https://doi.org/10.1007/JHEP10(2014)046

Keywords

Beyond Standard Model
QCD
Gauge Symmetry