Research in this direction, I have not seen. If there is a scattering of light by vacuum fluctuations of the electromagnetic field, it should be the scattering of light by light. Relativistic effects here are not necessary to consider the problem in the framework of the non-relativistic physics.
Light-by-light scattering in vacuum is predicted by QED (Euler-Heisenberg lagrangian). But it is a tiny effect. For a starting point see the linked page.
https://en.wikipedia.org/wiki/PVLAS
Kåre, you are right, but I surmise this is supposed to be known. Funny, how the mind corrects the question.
If there is a scattering of light by vacuum fluctuations of the electromagnetic field, it is the scattering of light by light.
The second statement is strange. There is no frame in which light is not relativistic.
Thanks for the answer. Yes, the interaction of light with the vacuum is known studies. I am also interested in the scattering of a photon by photon vacuum without participation. For example, the scattering of two crossed laser beams at their joint interaction with the electron
In other words. Can I get the scattering of a photon by photon solving the Schrödinger equation for the electron that interacts with two quantized electromagnetic fields (eg intersecting laser beams)
Obviously, in this case the scattering becomes. It is strange, but research in this area, I did not see, or very few of them.
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