  We consider the Heisenberg-Euler action for an electromagnetic field in
vacuum, which includes quantum corrections to the Maxwell equations induced by
photon-photon scattering. We show that, in some configurations, the plane
monochromatic waves become unstable, due to the appearance of secularities in
the dynamical equations. These secularities can be treated using a multiscale
approach, introducing a slow time variable. The amplitudes of the plane
electromagnetic waves satisfy a system of ordinary differential nonlinear
equations in the slow time. The analysis of this system shows that, due to the
effect of photon-photon scattering, in the unstable configurations the
electromagnetic waves oscillate periodically between left-hand-sided and
right-hand-sided polarizations. Finally, we discuss the physical implications
of this finding, and the possibility of disclosing traces of this effect in
optical experiments.
