Ternary Z2 x Z3 graded algebras and ternary Dirac equation
arXiv:1801.01403 · doi:10.1134/S1063778818060212
Abstract
The wave equation generalizing the Dirac operator to the Z3-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 Z2 x Z2 x Z3. 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) x U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.
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