2023/08/28 by Qiang Tang, Tang, Qiang, Jau Tang +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2308.14768
openalex publication_date 2023/08/28 · openalex created_date 2023/09/01 · openalex updated_date 2026/07/28
In this work, we analyze two models beyond the Standard Models descriptions that make ad hoc hypotheses of three point-like lepton and quark generations without explanations of their physical origins. Instead of using the same Dirac equation involving four anti-commutative matrices for all such structure-less elementary particles, we consider in the first model the use of sixteen direct-product matrices of quaternions that are related to Diracs gamma matrices. This associative direct-product matrix model could not generate three fermion generations satisfying Einsteins mass-energy relation. We show that sedenion algebra contains five distinct quaternion sub-algebras and three octonion sub-algebras but with a common intersecting quaternion algebra. This model naturally leads to precisely three generations as each of the non-associative octonion sub-algebra leads to one fermion generation. Moreover, we demonstrate the use of basic sedenion.