In the weak field limit, this becomes It describes photon–photon scattering in QED; Robert Karplus and Maurice Neuman calculated the full amplitude,[2] which is very small.
[4] Light-by-light scattering can be studied using the strong electromagnetic fields of the hadrons collided at the LHC,[5][6] and its observation was reported by the ATLAS Collaboration in 2019.
[7] PVLAS is searching for vacuum polarization of laser beams crossing magnetic fields to detect effects from axion dark matter.
In 2016 a team of astronomers from Italy, Poland, and the U.K. reported[8][9] observations of the light emitted by a neutron star (pulsar RX J1856.5−3754).
The star is surrounded by a very strong magnetic field (1013 G), and birefringence is expected from the vacuum polarization described by the Euler–Heisenberg Lagrangian.
Fan et al. pointed that their results are uncertain due to low accuracy of star model and the direction of the neutron magnetization axis.