Triality selection rules of Octonion and Quantum Mechanics

TL;DR

This paper explores the application of Cartan's supersymmetric model using Clifford algebra and octonions to describe particle interactions, decay processes, and cosmological matter composition, linking mathematical structures to dark matter and dark energy.

Contribution

It introduces a novel framework employing octonions and supersymmetric transformations to analyze particle interactions and cosmological phenomena.

Findings

Higgs decay into four photons is suppressed, but two-photon decay diagrams are present.

Approximately 23% of matter is interpreted as dark matter based on transformations.

About 2/3 of total matter corresponds to dark energy, aligning with experimental data.

Abstract

We apply the Cartan's supersymmetric model to the electromagnetic and weak interaction of leptons and hadrons, and study dynamics of $\pi^0,\eta,\eta'$ 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 $\Phi=\bar\phi\phi$, 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.