Ternary Z2 x Z3 graded algebras and ternary Dirac equation

Richard Kerner

doi:10.1134/s1063778818060212

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arXiv · 1801.01403

Ternary Z2 x Z3 graded algebras and ternary Dirac equation

Richard Kerner

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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.

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Richard Kerner. 2017-12-15. Ternary Z2 x Z3 graded algebras and ternary Dirac equation. https://doi.org/10.1134/s1063778818060212

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