A wave equation including leptons and quarks for the standard model of quantum physics in Clifford Algebra

Abstract

A wave equation with mass term is studied for all particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks $u$ and $d$ with three states of color and antiquarks $\overline{u}$ and $\overline{d}$. This wave equation is form invariant under the $C{l}_3^{\ast }$ group generalizing the relativistic invariance. It is gauge invariant under the $U(1)\times SU(2)\times SU(3)$ group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra $C{l}_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.