Planar QED in magnetic or electric solitonic backgrounds

We review the resolvent technique for computing the effective action in pla nar QED. For static magnetic backgrounds the effective action yields (minus ) the effective energy of the fermions, while for electric backgrounds the imaginary part of the effective action gives (half) the probability of ferm ion-antifermion pair creation. For some special "solitonic" background prof iles, these effective actions can be computed exactly.