Domain Wall Fermion Lattice Simulation in Quaternion Basis

TL;DR

This paper explores the use of quaternion and octonion algebra in lattice QCD simulations, highlighting the role of triality symmetry in various quantum chromodynamics phenomena.

Contribution

It introduces a quaternion basis approach to QCD analysis and discusses the implications of octonion triality symmetry in particle physics.

Findings

Triality symmetry influences proton charge form factor

Octonion algebra provides new insights into gluon self-energy

Quaternion basis offers a novel framework for QCD simulations

Abstract

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.