Schwinger pair production in electric and magnetic fields

Charged particles in static electric and magnetic fields have Landau levels and tunneling states from the vacuum. Using the instanton method of Phys. Rev. D 65, 105002 (2002), we obtain the formulas for the pair-production rate in spinor and scalar QED, which sum over all Landau levels and recover exactly the well-known results. The pair-production rates are calculated for an electric field of finite extent, and for the Sauter potential, both with a constant magnetic field also present, and are shown to have finite-size effects.