We point out a somewhat mysterious appearance of representations,
which exhibit the behaviour of three full generations of standard model
particles. These representations are found in the Clifford algebra
, 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 within it. These 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, : . The entire result is achieved using only the eight-dimensional
complex octonions as a single ingredient.
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.