  The standard model prediction for a magnetic dipole moment of a neutrino is
proportional to the neutrino mass and extremely small. It also generates a
flavor-changing process, but the GIM mechanism reduces the corresponding
amplitude. These properties of a neutrino magnetic moment change drastically in
a degenerate electron plasma. We have shown that an electron-hole excitation
gives a contribution proportional to the electrons' Fermi momentum. Since this
effect is absent in \(\mu\) and \(\tau\) sector, the GIM cancellation does not
work. The magnetic moment induces a neutrino oscillation if a strong enough
magnetic field exists in the plasma. The required magnitude of the field
strength that affects the \nue\ burst from a supernova is estimated to be the
order of \(10^8 \) Gauss.
