2022/04/27 by Juan Camilo Vélez Quiñones, Quiñones, Juan Camilo Vélez
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2205.06657
openalex publication_date 2022/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is set manifest an underlying algebraic structure of Dirac equation and solutions, in terms of Cl2 Clifford algebra projectors and ladder operators. From it, a scheme is proposed for constructing unified field theories by enlarging the pointed algebra. A toy unified matter field model is formulated, modifying Dirac equation with complex quaternions and octonions. The result describes a set of fermion fields with reminiscent properties of one standard model particle generation, exhibiting U(1) electromagnetism, SU(2) flavor and SU(3) color like symmetries, remarkably SU(2) induces frame fields, though further explorations are needed.