  In 1936, Weisskopf 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 \(\vec{E}^2-\vec{B}^2\) and
\(\vec{B}\cdot\vec{E}\). 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 \(\delta=e^2/(12\pi)\) for spinor
QED, and \(\delta_S=\delta/4\) for scalar QED.
