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Generations: three prints, in colour

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  • Published: 07 October 2014
  • volume 2014, Article number: 46 (2014)
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Generations: three prints, in colour
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  • Cohl Furey1,2 
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A preprint version of the article is available at arXiv.

Abstract

We point out a somewhat mysterious appearance of SUc(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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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Cohl Furey

  2. University of Waterloo, Ontario, N2L 3G1, Canada

    Cohl Furey

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  1. Cohl Furey
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Correspondence to Cohl Furey.

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ArXiv ePrint: 1405.4601

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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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

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Keywords

  • Beyond Standard Model
  • QCD
  • Gauge Symmetry

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