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I recently became interested in a notion of infraparticles as "true" scattering states in, for example, QED.

It is well known that S-matrix elements in QED suffer from infrared divergences due to soft virtual photons, which is usually cured by assuming a lower bound on detected photon energy by our detectors and summing over all processes with soft on-shell photons added to our out-states; yet this picture has its problems, such as whether one can tend this lower bound to 0, and if it is possible, what would one actually measure in the limit? As I understood (if I am wrong, please correct me), another way to solve this problem would be to redefine asymptotic states to add to an electron a "photon cloud" of some sorts, and while they are a bi different from usual LSZ-like particles (say, in terms of spectral measure they do not really correspond to poles), for them one can define cross-sections and all that; and looks like these states were even constructed in non-relativistic QED as something like "electron followed by a coherent state of photon field".

I am looking for references on this topic; I am familiar with the existence of Chen-Froehlich-Pizzo articles (say, this one https://arxiv.org/abs/0709.2812), but they have with all the rigor and functional analysis. I am not afraid of maths, but I would like to understand a more physical picture first, so if anyone is familiar with such references, I'd very appreciate it.

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    $\begingroup$ The issue with the Chen-Froehlich-Pizzo article you tried to read is perhaps not only the heavy math(s) but the fact it is a research article written for experts. You might find a more gentle discussion of infraparticles in the last section on scattering of the lectures by Dybalski www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/WojciechDybalski/… $\endgroup$ May 12, 2020 at 20:07
  • $\begingroup$ @AbdelmalekAbdesselam thanks a lot, that was a helpful reference! Yet I am looking for something maybe a little more thorough, still in a more "digested" form like lectures rather than research articles, but covering the notion in more detail. Are you perhaps familiar with something like this? $\endgroup$ May 13, 2020 at 8:26
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    $\begingroup$ Unfortunately, that reference by Dybalski is the best that I know. Others might have better expositions to recommend. $\endgroup$ May 13, 2020 at 17:31

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