2019/04/05 by Adam B. Gillard, Niels G. Gresnigt · 1 voice · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1140/epjc/s10052-019-6967-1
published as Eur. Phys. J. C (2019) 79: 446 · 22 pages, 2 figures
arxiv created 2019/04/05 · arxiv published 2019/04/05 · arxiv updated 2019/05/31
We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry SU(3)c× U(1)em can be described using the algebra of complexified sedenions ℂ⊗\mathbbS. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of ℂ⊗\mathbbS can be used to uniquely split the algebra into three complex octonion subalgebras ℂ⊗ \mathbbO. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 ℂ-dimensional ℂ⊗ \mathbbO subalgebras on themselves generates three copies of the Clifford algebra Cℓ(6). It was previously shown that the minimal left ideals of Cℓ(6) describe a single generation of fermions with unbroken SU(3)c× U(1)em gauge symmetry. Extending this construction from ℂ⊗\mathbbO to ℂ⊗\mathbbS naturally leads to a description of exactly three generations.