2018/08/24 by N. Furey · 80 citations
Mathematics · Physics and Astronomy · #Action (physics) #Algebra over a field #Algebraic and Geometric Analysis #Charge (physics) #Clifford algebra #Computer science #Gauge (firearms) #Gauge boson #Gauge theory #Geometry #Homogeneous space #Lepton #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Quark #Space (punctuation) #Standard Model (mathematical formulation) #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.physletb.2018.08.032
published in Physics Letters B 785, 84-89 (Elsevier BV) · 10 pages, 2 figures
openalex publication_date 2018/08/24 · openalex created_date 2018/08/31 · arxiv created 2019/10/17 · arxiv updated 2019/10/21 · openalex updated_date 2026/08/05
A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1) action which splits this 64C-dimensional space into complexified generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, [1], by incorporating electric charge.