  We discuss fermion pair productions in strong electric and magnetic fields.
We point out that, in the case of massless fermions, the vacuum persistency
probability per unit time and volume is zero in the strong electric and
magnetic fields, while it is finite when the magnetic field is absent. The
contribution from the lowest Landau level (LLL) dominates this phenomenon. We
also discuss dynamics of the vacuum decay, using an effective theory of the LLL
projection, taking into account the back reaction.
