QED Effective Action in Magnetic Field Backgrounds and Electromagnetic Duality

In the in-out formalism we advance a method of the inverse scattering matrix for calculating effective actions in pure magnetic field backgrounds. The one-loop effective actions are found in a localized magnetic field of Sauter type and approximately in a general magnetic field by applying the uniform semiclassical approximation. The effective actions exhibit the electromagnetic duality between a constant electric field and a constant magnetic field and between $E(x) = E sech^2 (x/L)$ and $B(x) = B sech^2 (x/L)$.

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