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I've been studying QFT for a couple of years now, and until today I haven't encountered any of the phenomena that I've studied in my QM course: tunneling, entanglement, probability measurements and this sort of things were lying low in my memory, almost forgotten.
Those phenomena are well observed and studied using QM: I reckon they can also be explained using QFT, but how?

For the comments: by "explain" I mean "use the tools of QFT (time-ordered products of fields, Feynman diagrams) to predict this behavior".

Mauro Giliberti
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  • Could you clarify what you mean "explain"? Are you looking for some additional understanding of these phenomena due to QFT being a more complete theory? Are you asking if their "paradoxical" nature vanishes? Or are you asking how these notions that you've encountered in QM can be reproduced in the QFT framework? – Nihar Karve Mar 04 '21 at 16:47
  • @NiharKarve please see the edited question. I guess I'm looking for a mix of the first and third questions that you proposed. – Mauro Giliberti Mar 04 '21 at 18:22
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    I don't really understand this question - QFT is a quantum mechanical theory and hence has precisely the same concepts of entanglement or probability as the basic non-relativistic quantum mechanics of particles we usually learn first. I'm also not sure what you mean by "tunneling" in this context, or rather what you think there is to explain. – ACuriousMind Mar 04 '21 at 18:28
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    If what you really want to ask is how specific predictions of non-relativistic QM with fixed particles are compatible with those of relativistic QFT, the answer is that rQFT reduces to nrQM in a suitable limit (depending on the specific application) and we already have plenty of questions about such limits, see e.g. https://physics.stackexchange.com/q/142159/50583 – ACuriousMind Mar 04 '21 at 18:31
  • Are you uninterested in the Lamb shift or the anomalous magnetic moment of the electron? – Cosmas Zachos Mar 04 '21 at 19:16
  • @ACuriousMind by "tunneling" I mean what is written in the "quantum-tunneling" tag. And while I agree that QFT is a quantum theory, it doesn't have precisely the same features (otherwise we wouldn't have left the non-relativistic QM). For example, I've read that quantum tunneling doesn't happen in (3+1)D QFT because a double finite well potential will give SSB, while in (1+0)D QM there is no SSB precisely because the particle can tunnel from one well to the other. Is it sufficient to twist the dimensions of QFT to get back to QM in this case, or is there something more? – Mauro Giliberti Mar 08 '21 at 00:06
  • That's a question rather specific to tunneling/SSB, discussed e.g. in https://physics.stackexchange.com/q/321698/50583 - it is not a difference in how they treat probabilities or anything, it's that the potential barrier in an infinite-volume QFT is infinitely high, different from the finite potential barrier in a QM potential well. – ACuriousMind Mar 08 '21 at 08:43

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