  We write the neutrino mass eigenstate into the weak doublet of the group
$SU(2)_L$ . The massive neutrino is written as the mixture of the flavor
neutrino. The flavor changing Lagrangian of lepton-W boson coupling were
obtained. The neutrino mixing angle appear in the vertex factor of the
interaction of flavor neutrino with charged lepton. The results lead to the
Feynman diagram of neutrino oscillation in matter and play an important role in
$(\nu_e -e)$ elastic scattering . The anomalous muon decay $\mu^-\rightarrow
e^-+\overline{\nu}_\mu+\nu_e$ take part in giving the muon decay lifetime of
$2.197019 \mu s$ . The branching ratio $B(\mu^-\rightarrow
e^-+\overline{\nu}_\mu+\nu_e)$ is obtained.
