Generalization of the Dirac equation admitting isospin and color symmetries (Q1090862)

Relativistically invariant wave equations to describe elementary particles cannot yield internal quantum numbers like isospin although they give rise to observables like spin. Many efforts in the past were made to find a larger symmetry group containing both the Lorentz and the internal symmetry group. All these efforts floundered as they were bound to, according to O'Raffertaigh's theorem. The other path open was taken by the gauge theorists. The author attempts to obtain a Dirac like equation for particles, which yield a unified description of all quarks and elementary particles. This is done by complexifying the space time algebra, which is a Clifford algebra, explicitly build in an asymmetry in the handedness, and study the associated matrix representations. The mass term appears as an interaction between fields with opposite handedness. A Lagrangian formulation is also presented. Asymptotic freedom and confinement are also studied. The style of the paper makes it very unclear. The level of mathematical rigour is that of usual papers in particle physics.