Generations: three prints, in colour
Journal of High Energy Physics
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Furey, C. (2014). Generations: three prints, in colour. Journal of High Energy Physics https://doi.org/10.1007/JHEP10(2014)046
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.
Beyond Standard Model, QCD, Gauge Symmetry
The author is indebted to S. Farnsworth, G. Fiore, L. Smolin, and C. Tamarit for their feedback on this work. This research was supported by the Templeton Foundation, and – 8 – JHEP10(2014)046 also in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
External DOI: https://doi.org/10.1007/JHEP10(2014)046
This record's URL: https://www.repository.cam.ac.uk/handle/1810/254701
Attribution 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by/2.0/uk/
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