Leptons: charged and uncharged (neutrinos) inside a proposal for a geometrical model some considerations

Abstract

We study the leptons in two different settings, first with the standard theory and second in a geometrical model. All the leptons with no null masses. The starting point in the Dirac equation. We examine in detail the roles of the spin, of the helicity and of the chirality. We emphasize the non symmetrical aspect in the relation of the helicity with the chirality. This has an important implication in the statistical interpretation and it is most relevant in the dilemma matter antimater for the uncharged leptons. We show a solution of the Dirac equation which seems appropriate for the neutrinos. In our studies, geometric structure of the leptons and the quarks, we distinguish a spin as a scalar (up , down) and as a vector. For the charged leptons: the spin (vector) is at every instant in a plane perpendicular to the vector that represents the momentum. The magnetic moment and the spin (a vector) are proportional. For the uncharged leptons: the intrinsic properties driving to an electromagnetic interaction, even if it is of a very low intensity (absence of electric charge). There are minor modifications appearing as radiative corrections, perhaps the origin for magnetic and electric moments. We propose, tentatively, a mechanism for explaining the oscillations of the uncharged leptons. Our presentation is not standard, suggesting further research at several points (still many possible questions).