In 1936, Weisskopf [K. Dan. Vidensk. Selsk. Mat. Fys. Medd. XIV (1936)] showed that for vanishing electric or magnetic fields the strong-field behavior of the one-loop Euler-Heisenberg effective Lagrangian of quantum electro dynamics (QED) is logarithmic. Here we generalize this result for different limits of the Lorentz invariants E⃗ 2−B⃗ 2 and B⃗ ·E⃗ . The logarithmic dependence can be interpreted as a lowest-order manifestation of an anomalous power behavior of the effective Lagrangian of QED, with critical exponents δ=e2/(12π) for spinor QED, and δS=δ/4 for scalar QED.
