  Vacuum instability of the strong electromagnetic field has been discussed
since long time ago. The instability of the strong electric field due to
creation of electron pairs is one of the examples, which is known as Schwinger
process. What matters are the coupling of particles to the electromagnetic
field and the mass of the particle to be produced. The critical electric field
for electrons in the minimal coupling is ~ m^2/e . Spin 1/2 neutral particles
but with magnetic dipole moments can interact with the electromagnetic field
through Pauli coupling. The instability of the particular vacuum under the
strong magnetic field can be formulated as the emergence of imaginary parts of
the effective potential. In this talk, the development of the imaginary part in
the effective potential as a function of the magnetic field strength is
discussed for the configurations of the uniform magnetic field and the
inhomogeneous magnetic field. Neutrinos are the lightest particle(if not photon
or gluon) in the "standard model", of which electromagnetic property is poorly
known experimentally. Recently the observation of neutrino oscillation shows
the necessity of neutrino masses. It implies that the standard model is
subjected to be modified such that non-trivial electromagnetic structure of
neutrino should be reconsidered although they are assigned to be neutral. And
the possibility of anomalous electromagnetic form factor is an open question
theoretically and experimentally. In this talk, the implication of
non-vanishing magnetic dipole moment of neutrinos is also discussed: the
instability of the strong magnetic field and the enhancement of neutrino
production in high energy collider experiments.
