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

Claude Daviau (1, 2) , Jacques Bertrand (1)

1 Chercheur indépendant
2 ECN - École Centrale de Nantes

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 $Cl_3^*$ 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 $Cl_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.

Mots clés: invariance group; Dirac equation; electromagnetism; weak interactions; strong interactions; Clifford algebras

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Claude Daviau, Jacques Bertrand. A wave equation including leptons and quarks for the standard model of quantum physics in Clifford Algebra. 2014. ⟨hal-01058706⟩