An exact QED3+1 effective action

We compute the exact QED3+1 effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. An asymptotic expansion of this exact effective action yields an all-orders derivative expansion, the first terms of which agree with independent derivative expansion computations. These results generalize analogous earlier results by Cangemi et al. in QED2+1.