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The basic question is "why light travels at slower speed in a medium?" I mean what's the full second quantization quantum mechanical explanation of the phenomenon? I'm looking for the explicit calculations on this, not only the "by words" explanation. I'm interested on visible light, so eV energy scale.
I've often heard that "the photon receives an effective mass" and "Maxwell equation modifies in the medium" and I indeed agree with theese kind of explanation, but the single little "simple" building blocks of the phenomenon remains obsure in my opinion. How we pass from the single photon view to a medium exitation? What's the basic QED phenomenon? Compton scatter? By who?
The effective mass raises more questions than answers: How the transition is made? Do we use Proca's equation inside the medium? In this case should be the longitudinal polarization of the quasiparticle, right?

I have also some related questions, in random order:

  • Does exist "simple" solvable models? maybe for diluite gas, perfect cubic lattice solid or something else
  • What phenomenology does them reproduce? on which hypothesis?
  • Does it depend on a thermodynamic limit of the medium (gas, liquid, solid)?
  • Fixing enviromental conditions (temperature, pressure etc.), does single photons interact always in the same way, if not absorbed or diffused? If not, why? and how much?
  • Does exists books or ref on such argument?

Thank you!

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  • $\begingroup$ I think polaritons are related to this, maybe a place to start. See for example physics.stackexchange.com/a/221235/40895 $\endgroup$ – user129412 Jul 11 '17 at 18:27
  • $\begingroup$ Of course. The problem is that googling polariton I was only able to find uncommon experimental condition or very specific cases, not a basic explanation of this. I'm really interested on passing from the usual massless free photon to the medium (massive?) excitation, in ordinary conditions. In general I've recived answers like "we pass from Maxwell equations to massive things" polaritons i think, "multi scatter from electrons or nuclei" and so on; each with some caveat and rising in me other questions. $\endgroup$ – SebaF_it Jul 11 '17 at 18:49
  • $\begingroup$ Right. For example in the answer I linked: "Under normal circumstances, e.g. light passing through glass, the interaction of the light and the medium is relatively weak and we probably wouldn't use a polariton description. Instead we'd use a classical description...". You'd, for example, like to know how this situation is handled in second quantization. $\endgroup$ – user129412 Jul 11 '17 at 18:58
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    $\begingroup$ That's the point! I myself have received the question and after some days of thinking the answer is "I don't really know". So here I am. $\endgroup$ – SebaF_it Jul 11 '17 at 19:07
  • $\begingroup$ Don't think so. Certainly an explanation, I've found a lot of such level, but I'm really looking for a post graduate level one. I'd be happy even if someone knows books or review on this in order to study on my own. $\endgroup$ – SebaF_it Jul 12 '17 at 7:54