Abstract
The conservation of lepton number is assumed to be associated with a general Yang–Mills (gYM) 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 nonzero masses. Thus, gYM 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.