三元Z2 x Z3分次代数与三元Dirac方程
Ternary Z2 x Z3 graded algebras and ternary Dirac equation
摘要：
将狄拉克算子推广到Z3阶情形的波动方程，其对角化导致一个六阶方程。它不仅纠缠夸克和反夸克态以及“u”和“d”夸克，而且还纠缠三种颜色，因此在乘积群Z2 x Z2 x Z3下是不变的。该方程的解不能传播，因为它们的指数总是包含非振荡的实阻尼因子。然而，我们展示了某些立方积如何传播。该模型提出了色SU（3）对称性和SU（2）× U（1）的起源，它们在该模型中自动出现，导致标准模型的完整玻色子规范扇区。
英文摘要：
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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