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Neutrino Oscillation, Finite Self-Mass and General Yang-Mills Symmetry

The conservation of lepton number is assumed to be associated with a general Yang-Mills symmetry. New transformations involve (Lorentz) vector gauge functions and characteristic phase functions, and they form a group. General Yang-Mills fields are associated with new fourth-order equations and linear potentials. Lepton self-masses turn out to be finite and proportional to the inverse of lepton masses, which implies that neutrinos should have non-zero masses. Thus, general Yang-Mills symmetry could provide an understanding of neutrino oscillations and suggests that neutrinos with masses and very weak leptonic force may play a role in dark matter.