Triality selection rules of Octonion and Quantum Mechanics

Abstract

We apply the Cartan's supersymmetric model to the electromagnetic and weak interaction of leptons and hadrons, and study dynamics of ${\pi }^0,\eta ,{\eta }^{\prime }$ meson and Higgs boson. We adopt the Clifford algebra, express Pauli spinors by quaternions, Dirac spinors by octonions, and take into account the supersymmetric transformations $G_{ij}$ and $G_{ijk}$ of Cartan. When Higgs boson is assigned as Cartan's spinor pairs $\Psi =\bar{\psi }\psi$ or $\Phi =\bar{\varphi }\varphi$, its decay into $\gamma \gamma \gamma \gamma$ does not occur, but there appear 8 diagrams of $\Psi \to \gamma \gamma$ and 8 diagrams of $\Phi \to \gamma \gamma$. If our world matter makes 4.6\% of the total matter, and we can interpret the matter transformed by $G_{23},G_{12},G_{123},G_{13},G_{132}$ or about 5 times of our matter, i.e. 23\% corresponds to dark matter. We can assign the world transformed by $G_{12},G_{123},G_{13}$ and $G_{132}$, which make about 2/3 of the total corresponds to the dark energy. Experimentally, 72\% of the total matter corresponds to dark energy.

28 pages, 52 figures, RIKEN workshop 4th Sept. 2014

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