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

Fast vacuum decay into particle pairs in strong electric and magnetic fields