  In high energy heavy ion collisions as well as in astrophysical objects like
magnetars extreme magnetic field strengths are reached. Thus, there exists a
need to calculate divers QED processes to all orders in the magnetic field. We
calculate the vacuum polarization graph in second order of the electric field
and all orders of the magnetic field resulting in a generalization of the
Euler-Heisenberg Lagrangian. We perform the calculation in the effective
Lagrangian approach of J. Schwinger as well as using modified Feynman rules. We
find that both approaches give the same results provided that the different
finite renormalization terms are taken into account. Our results imply that any
quantitative explanation of the recently proposed Chiral Magnetic Effect has to
take 'Strong QED' effects into account, because these corrections are huge.
