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Description of  The 3 Generations of Elementary Particles

Abstract In our earlier paper [A1] we saw that Quantum Theory emerges when we construct a scaled metric by simply multiplying the metric with a factor F[f], thereby assuming the inner part of the scale factor to be an arbitrary function f. f itself then – so it was derived – becomes the wave function**. Subjecting this scaled metric in the usual way to the Einstein-Hilbert action [A2] does not only present us with Quantum Einstein-Field-Equations [A3] and thus, a quantized version of Einstein’s General Theory of Relativity [A4], but – along the way (e.g. [A5 – A10]) – gives us all classical and non-classical quantum equations, including Schrцdinger, Klein-Gordon and Dirac. Also, thermodynamics can be derived from, respectively found inside this simple scaled metric approach [A3, A10]. Now in our last paper of this series [A1], we saw that there are apparently several paths to come up with an explanation for the existence of the generations of elementary particles. None of these explanations, however, was truly satisfying and so we concluded the abstract to [A1] with the words: “Thus, so our current conclusion, the way to solve the 3 generations problem [A11] could be outlined here but – so far – this path was not treated in a manner one could call complete.” Here now we want to move on in applying the scaled metric approach and by combining it with the Hilbert concept [A2] of the variated Ricci scalar, only that this time, we do not only look for the variation with respect to the metric tensor but go a bit broader, we think that we have found the answer. ** For convenience we will repeat these derivations for the Klein-Gordon, the Schrцdinger and the Dirac equation in the appendices of this paper.