The quantification of the kinetic momentum of electrons, neutrinos, protons and neutrons with the $\hbar/2$ value is consequence of the extended relativistic invariance of the wave of fundamental particles with spin $1/2$. The reasons of this logical link use only properties of the waves, which are functions of space-time with value into the multiplicative Lie groups $Cl_3^*$ and $\mathrm{End}(Cl_3)$. Space-time is a manifold included into the auto-adjoint part of $Cl_3^*$. The Lagrangian densities are the Cliffordian real parts of the wave equations. The equivalence between invariant wave equation and Dirac form of the wave equation has the form of Lagrange's equations. The momentum-energy tensor linked by the Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under $Cl_3^*$ of the kinetic momentum tensor gives eight vectors. One of these vectors has a space-time length with value $\hbar/2$. This satisfies many aspects of the standard model of quantum physics and of the relativistic theory of gravitation.