One generation of standard model Weyl representations as a single copy of R⊗C⊗H⊗O

Abstract

Peering in from the outside, A:=R⊗C⊗H⊗O looks to be an ideal mathematical structure for particle physics. It is 32 C-dimensional: exactly the size of one full generation of fermions. Furthermore, as alluded to earlier in [1], it supplies a richer algebraic structure, which can be used, for example, to replace SU(5) with the SU(3)×SU(2)×U(1)/Z6 symmetry of the standard model.However, this line of research has been weighted down by a difficulty known as the fermion doubling problem. That is, a satisfactory description of SL(2,C) symmetries has so far only been achieved by taking two copies of the algebra, instead of one. Arguably, this doubling of states betrays much of A's original appeal. In this article, we solve the fermion doubling problem in the context of A.Furthermore, we give an explicit description of the standard model symmetries, Image 1, its gauge bosons, Higgs, and a generation of fermions, each in the compact language of this 32 C-dimensional algebra. Most importantly, we seek out the subalgebra of Image 1 which is invariant under the complex conjugate - and find that it is given by su(3)C⊕u(1)EM. Could this new result provide a clue as to why the standard model symmetries break in the way that they do?