Quaternion Octonion Reformulation of Quantum Chromodynamics

TL;DR

This paper develops a quaternionic and octonionic reformulation of Yang-Mills equations and quantum chromodynamics, providing a new algebraic perspective on gauge symmetries in particle physics.

Contribution

It introduces a novel quaternionic and octonionic framework for Yang-Mills fields and QCD, linking algebraic structures to gauge symmetries.

Findings

Quaternion units explain Yang-Mills field structure.

Octonion units model SU(3) gauge symmetry.

Unified algebraic description of gauge fields.

Abstract

We have made an attempt to develop the quaternionic formulation of Yang - Mill's field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang- Mill's field while the seven octonion units provide the consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics.