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.
Highlights
The aim of this work is to construct with the same logic and mathematical rigour of General Relativity (GR), aHow to cite this paper: Daviau, C., Bertrand, J. and Girardot, D. (2016) Towards the Unification of All Interactions (The First Part: The Spinor Wave)
The U (1) × SU (2) part of the gauge group acts on electron + neutrino
Our study proves that it is general: the numeric equations equivalent to the wave equations of the “matter” may be split into two parts: a dynamical part containing rotational-like terms, and a conservative part containing divergence-like terms, and the conservative part is a consequence of the dynamical equations
Summary
The aim of this work is to construct with the same logic and mathematical rigour of General Relativity (GR), a. Numerous and complicated attempts with quantum groups, strings, branes and many supplementary dimensions, supergravity, loop quantum gravity, were developed All these attempts were based on the methods of the second quantization and were based upon the non-relativistic Schrödinger equation. All calculations are there made with mathematical rigour [7] and with very accurate experimental results Another reason of this work is the study of the finite representations of the Lorentz proper group [18]: relativistic quantum mechanics uses not the Lorentz group but another one, in a way which is not a consequence of the principles of the theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
