Domain Wall Fermion Lattice Simulation in Quaternion Basis

In the QCD analysis, when quarks are expressed in quaternion basis, the quark and its charge conjugate together are expressed by octonions and the octonion posesses the triality symmetry. Gluos are expressed by Pl\"ucker coordinates of spinors. Roles of triality in the proton charge form factor, three loop gluon self energy, technicolor, fine tuning and unparticle physics are discussed.Comment: 3 pages, 6 figures, QCHS-09(Madrid, August 30-Sept 3, 2010) proceeding

The Color Antisymmetric Ghost Propagator and One-Loop Vertex Renormalization

The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Implications for the Kugo-Ojima color confinement and the QCD running coupling are discussed.Comment: 16 pages, 20 figures, typos corrected, version to be published in Prog. Theor. Phys. vol.119, No.

Triality selection rules of Octonion and Quantum Mechanics

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.Comment: 28 pages, 52 figures, RIKEN workshop 4th Sept. 201

Chiral Symmetry and BRST Symmetry Breaking, Quaternion Reality and the Lattice Simulation

We discuss that the deviation of the Kugo-Ojima color confinement parameter $u(0)$ from -1 in the case of quenched lattice simulation and the consistency with -1 in the case of full QCD simulation could be attributed to the boundary condition defined by fermions inside the region of $r<1$fm. By using the domain wall fermion propagator in lattice simulation, we show that the chiral symmetry breaking in the infrared can become manifest when one assumes that the left-handed fermion on the left wall and the right-handed fermion on the right wall are correlated by a self-dual gauge field. The relation between the infrared fixed point of the running coupling measured in lattice simulations, the prediction of the BLM renormalization theory, the conformal field theory with use of the t'Hooft anomaly matching condition in non-SUSY supersymmetric theory and the quaternion real condition are discussed.Comment: 3 pages 2 figures, submitted to the SCGT09 proceeding