Abstract
Describing a wave with spin 1/2, the Dirac equation is form invariant under \({SL(2,\mathbb{C})}\), subgroup of \({Cl_3^*=GL(2,\mathbb{C})}\) which is the true group of form invariance of the Dirac equation. Firstly we use the Cl 3 algebra to read all features of the Dirac equation for a wave with spin 1/2. We extend this to electromagnetic laws. Next we get the gauge group of electro-weak interactions, first in the leptonic case, electron+neutrino, next in the quark case. The complete wave for all objects of the first generation uses the Clifford algebra Cl 1,5. The gauge group is then enlarged into a \({U(1)\times SU(2)\times SU(3)}\) Lie group. We consolidate both the standard model and the use of Clifford algebras, true mathematical frame of quantum physics.
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All my thanks go to Jacques Bertrand who helped me to develop the present work.
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Daviau, C. Gauge Group of the Standard Model in Cl 1,5 . Adv. Appl. Clifford Algebras 27, 279–290 (2017). https://doi.org/10.1007/s00006-015-0566-5
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DOI: https://doi.org/10.1007/s00006-015-0566-5