Towards the Unification of All Interactions (The First Part: The Spinor Wave)

Abstract

For the unification of gravitation with electromagnetism, weak and strong interactions, we use a unique and very simple framework, the Clifford algebra of space . We enlarge our previous wave equation to the general case, including all leptons, quarks and antiparticles of the first generation. The wave equation is a generalization of the Dirac equation with a compulsory non-linear mass term. This equation is form invariant under the group of the invertible elements in the space algebra. The form invariance is fully compatible with the gauge invariance of the standard model. The wave equations of the different particles come by Lagrange equations from a Lagrangian density and this Lagrangian density is the sum of the real parts of the wave equations. Both form invariance and gauge invariance are exact symmetries, not only partial or broken symmetries. Inertia is already present in the part of the gauge group and the inertial chiral potential vector simplifies weak interactions. Relativistic quantum physics is then a naturally yet unified theory, including all interactions.