TITLE:
Geometry of the Standard Model of Quantum Physics
AUTHORS:
Claude Daviau, Jacques Bertrand
KEYWORDS:
Geometry of the Standard Model of Quantum Physics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.1,
January
28,
2015
ABSTRACT: General relativity links gravitation to the
structure of our space-time. Nowadays physics knows four types of interactions:
Gravitation, electromagnetism, weak interactions, strong interactions. The
theory of everything (ToE) is the unification of these four domains. We study
several necessary cornerstones for such a theory: geometry and mathematics,
adapted manifolds on the real domain, Clifford algebras over tangent spaces of
these manifolds, the real Lagrangian density in connection with the standard
model of quantum physics. The geometry of the standard model of quantum physics
uses three Clifford algebras. The algebra of the 3-dimensional
physical space is sufficient to describe the wave of the electron. The algebra of space-time is sufficient
to describe the wave of the pair electron-neutrino. A greater space-time with
two 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 wave
equations for the two other generations. Values of these waves allow defining,
in each point of space-time, geometric transformations from one intrinsic
manifold of space-time into the usual manifold. The Lagrangian density is the
scalar part of the wave equation.