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We review the resolvent technique for computing the effective action inplanar QED. For static magnetic backgrounds the effective action yields (minus)the effective energy of the fermions, while for electric backgrounds theimaginary part of the effective action gives (half) the probability offermion-antifermion pair creation. For some special `solitonic' backgroundprofiles, these effective actions can be computed exactly.

Planar QED in Magnetic or Electric Solitonic Backgrounds