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General relativity links gravitation to thestructure of our space-time. Nowadays physics knows four types of interactions:Gravitation, electromagnetism, weak interactions, strong interactions. Thetheory of everything ToE is the unification of these four domains. We studyseveral necessary cornerstones for such a theory: geometry and mathematics,adapted manifolds on the real domain, Clifford algebras over tangent spaces ofthese manifolds, the real Lagrangian density in connection with the standardmodel of quantum physics. The geometry of the standard model of quantum physicsuses three Clifford algebras. The algebra  of the 3-dimensionalphysical space is sufficient to describe the wave of the electron. The algebra of space-time is sufficientto describe the wave of the pair electron-neutrino. A greater space-time withtwo additional dimensions of space generates the algebra . It is sufficient to get the wave equation for all fermions,electron, its neutrino and quarks u and d of the first generation, and the waveequations for the two other generations. Values of these waves allow defining,in each point of space-time, geometric transformations from one intrinsicmanifold of space-time into the usual manifold. The Lagrangian density is thescalar part of the wave equation.


Geometry of the Standard Model of Quantum Physics

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Daviau, C. and Bertrand, J. 2015 Geometry of the Standard Model of Quantum Physics. Journal of Applied Mathematics and Physics, 3, 46-61. doi: 10.4236-jamp.2015.31007.

Author: Claude Daviau1, Jacques Bertrand2



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