2017/12/15 by Richard Kerner · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Dirac equation #Dirac operator #Equation of state #Gauge theory #Invariant (physics) #Mathematical physics #Nonlinear Waves and Solitons #Particle physics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Quark #Symmetry (geometry) #Ternary operation #Two-body Dirac equations #hep-th #math-ph #math.MP #physics.gen-ph
paper · pdf · doi:10.1134/s1063778818060212
22 pages, 7 figures; to appear in "Physics of Atomic Nuclei" ("Yadernaya Fizika", Russian journal), Proceedings of the 17th Conference "Symmetries in Physics", Yerevan, July 2017
arxiv created 2017/12/15 · openalex created_date 2018/01/12 · openalex publication_date 2018/11/01 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05
The wave equation generalizing the Dirac operator to the Z 3 -graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors, and is therefore invariant under the product group Z 2 × Z 2 × Z 3 . The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU (3) symmetry and of the SU (2) × U (1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.