  We revisit the time evolution of the lepton family number for a SU(2) doublet
consisting of a neutrino and a charged lepton. The lepton family number is
defined through the weak basis of the SU(2) doublet, where the charged lepton
mass matrix is real and diagonal. The lepton family number carried by the
neutrino is defined by the left-handed current of the neutrino family. For this
work we assume the neutrinos have Majorana mass. This Majorana mass term is
switched on at time $t=0$ and the lepton family number is evolved. Since the
operator in the flavor eigenstate is continuously connected to that of the mass
eigenstate, the creation and annihilation operators for the two eigenstates are
related to each other. We compute the time evolution of all lepton family
numbers by choosing a specific initial flavor eigenstate for a neutrino. The
evolution is studied for relativistic and nonrelativistic neutrinos. The
nonrelativistic region is of particular interest for the Cosmic Neutrino
Background predicted from big bang models. In that region we find the lepton
family numbers are sensitive to Majorana and Dirac phases, the absolute mass,
and mass hierarchy of neutrinos.
