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I am wondering whether there is a simple—or complicated—way to explain from a purely quantum mechanics (or QFT) viewpoint what happens to the photons when they go through some material whose index of refraction is greater than 1 (or complex if you want to take the case of a metal).

The explanation should therefore discard the use of "EM fields" because the light has to be quantized. The material should be thought as atoms or molecules I suppose.

I've been told that the explanation that says that photons are being absorbed by atoms and re-emitted with a slight delay and thus explaining why light is slower in a material compared to vacuum is wrong, because if the photons were absorbed and re-emitted the delay would be stochastic and so a laser beam entering a transparent material would leave the material at different times which is not observed in practice.

Qmechanic
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untreated_paramediensis_karnik
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    Even when we quantize light it stays a field. Quantum field theory deals with continuous objects. Individual quanta only come into play when we are doing preparation of or measurements on the field. You can, if you want to, ponder semi-classical models like scattering of individual photons on individual atoms or electrons, but what you are really doing in your mind there is to ad-hoc select terms from a QED perturbation series that you think should be physically dominant, but it's not the same as doing an actual ab-initio calculation (which, by the way, is way overkill). – CuriousOne May 06 '16 at 23:09
  • I see. I am not interested in using a semi-classical model though. On IRC I've been told, as answer to the question I posted that : "it's insanely complex to describe it in terms of quantum field theory" and "you must calculate the dressed propagator in a medium. That fills books". I wonder if this rings a bell to someone who could give more details on this. – untreated_paramediensis_karnik May 06 '16 at 23:17
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    Whoever said that on IRC was correct. You would be embarking on an insane program that would yield next to no useful physical predictions in return. For ordinary light/matter interactions semi-classical approximations are perfectly enough. There are choice problems in atomic physics where QED calculations are required to get the correct answer, but one would usually not attempt to perform the same level of analysis on an actual solid for the purposes of explaining the index of refraction of a material. I doubt you could even be successful for any but the most trivial systems. – CuriousOne May 06 '16 at 23:21
  • Having said that, there are attempts to use QFT methods on solids and they do fill books, but I am not the right person to ask. I hope you can find a theoretician who can tell you what systems this method is useful for and how you can get a "gentle" introduction to it. – CuriousOne May 06 '16 at 23:23
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    @CuriousOne Does this mean that from a purely quantum mechanics viewpoint, what happens is really too complicated to even describe in words? – untreated_paramediensis_karnik May 06 '16 at 23:27
  • @no_choice99: For a beginning, study this: http://physics.stackexchange.com/q/247084/ – Peter Diehr May 06 '16 at 23:51
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    "even describe in words?" Are you under the impression that words are easier? The situation is generally that describing any non-trivial process in words with precision* is much, much harder than doing the math. And the "easy" descriptions in words are always lossy and wrong. – dmckee --- ex-moderator kitten May 07 '16 at 00:01
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    The key thing here is that the photons interact coherently with the atoms. In quantum mechanics you can consider two opposite limits. At high energies you get inelastic interactions where the photon will change the state of the system it interacts with e.g. ionize or excite atoms. At low energies the proton can scatter off of atoms without changing the internal state of atoms and even without changing the center of mass motion of the atom. Interference between a photons interacting with different atoms is then possible as no "which way information" is left in the system by the interactions. – Count Iblis May 07 '16 at 00:05
  • @dmckee "even describe in words" I mean something like "if we make X, Y and Z assumptions and solve the Alpha equations we'd get that Beta holds as an approximation, etc." Since I do not seek a semi-classical explanation and from what I could understand of what I've been told, these kind of explanations are going to be extremely complex. – untreated_paramediensis_karnik May 07 '16 at 00:11
  • At at few eV to a couple hundred keV it's just not necessary to use the language of QFT, but you still need the correct models, even semi-classically, and that's a couple semesters worth of material, just for mostly elastic processes. For the nuclear stuff you better reserve a lifetime. – CuriousOne May 07 '16 at 00:14
  • Possible duplicates: http://physics.stackexchange.com/q/2041/2451 , http://physics.stackexchange.com/q/6428/2451 and links therein. – Qmechanic May 07 '16 at 03:36
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    Lubos Motl has a blog post describing how classical fields emerge from QFT . This may give you an idea of the complexity of calculations involved on the complicated solids problem http://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html – anna v May 07 '16 at 03:57

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