English

Triality selection rules of Octonion and Quantum Mechanics

High Energy Physics - Phenomenology 2015-06-25 v3

Abstract

We apply the Cartan's supersymmetric model to the electromagnetic and weak interaction of leptons and hadrons, and study dynamics of π0,η,η\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 GijG_{ij} and GijkG_{ijk} of Cartan. When Higgs boson is assigned as Cartan's spinor pairs Ψ=ψˉψ\Psi=\bar\psi\psi or Φ=ϕˉϕ\Phi=\bar\phi\phi, its decay into γγγγ\gamma\gamma\gamma\gamma does not occur, but there appear 8 diagrams of Ψγγ\Psi\to\gamma\gamma and 8 diagrams of Φγγ\Phi\to\gamma\gamma. If our world matter makes 4.6\% of the total matter, and we can interpret the matter transformed by G23,G12,G123,G13,G132G_{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 G12,G123,G13G_{12}, G_{123}, G_{13} and G132G_{132}, which make about 2/3 of the total corresponds to the dark energy. Experimentally, 72\% of the total matter corresponds to dark energy.

Keywords

Cite

@article{arxiv.1409.3761,
  title  = {Triality selection rules of Octonion and Quantum Mechanics},
  author = {Sadataka Furui},
  journal= {arXiv preprint arXiv:1409.3761},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T05:55:24.886Z