  Analytical calculations of radiative corrections in strong-field QED have
hinted that in the presence of an intense plane wave the effective coupling of
the theory in the high-energy sector may increase as the $(2/3)$-power of the
energy scale. These findings have raised the question of their compatibility
with the corresponding logarithmic increase of radiative corrections in QED in
vacuum. However, all these analytical results in strong-field QED have been
obtained within the limiting case of a background constant crossed field.
Starting from the polarization operator and the mass operator in a general
plane wave, we show that the constant-crossed-field limit and the high-energy
limit do not commute with each other and identify the physical parameter
discriminating between the two alternative limits orders. As a result, we find
that the power-law scaling at asymptotically large energy scales pertains
strictly speaking only to the case of a constant crossed background field,
whereas high-energy radiative corrections in a general plane wave depend
logarithmically on the energy scale as in vacuum. However, we also confirm the
possibility of testing the ``power-law'' regime experimentally by means of
realistic setups involving, e.g., high-power lasers or high-density
electron-positron bunches.
