Lepton numbers in the framework of neutrino mixing

In this short review we discuss the notion of lepton numbers. The strong evidence in favor of neutrino oscillations obtained recently in the super-Kamiokande atmospheric neutrino experiment and in solar neutrino experiments imply that the law of conservation of family lepton numbers L-e, L-mu and L-tau is strongly violated. We consider the flavor neutrinos v(e), v(mu), and v(tau) and we discuss the evolution of these states in space time in the case of nonconservation of family lepton numbers due to the mixing of light neutrinos. We discuss and compare different flavor neutrino discovery experiments. We stress that experiments on the search for v(mu) --> v(tau) and v(e) --> v(tau) oscillations demonstrated that the flavor neutrino v(tau) is a new type of neutrino, different from v(e) and v(mu). In the case of neutrino mixing, the lepton number (only one) is connected with the nature of massive neutrinos. Such a conserved lepton number exists if massive neutrinos are Dirac particles. We review possibilities to check in future experiments whether the conserved lepton number exists.