What are the mathematical relationships (if any) between the particles as described by Quantum Mechanics and the particles described by Quantum Field Theory? A specific question related to the general question above arose in post #14 of the thread: How can a particle be a combination of other particles? The two more specific questions paraphrased below were asked there, but failed to attract any answers. I am hoping that starting a separate thread on this question might attract some answers. 1. Is there a QFT about EM and photons? 2. If so, is there a theoretical or mathematical connection between such a QFT and the relativistic Maxwell equations that define the behavior of the EM fields? I found the following in post #2 on the thread: Relation between QM and QFT. QFT is the unification of special relativity and QM. In QM the basic ingredient are wavefunctions. In QFT the basic ingredient are fields of which the fluctuations correspond to particles.I also found the following in post #2 on the thread: Question on particles/fields in QFT You can consider each excitation of the field is a particle since each excitation is discrete and obeys the energy momentum relation E^2=p^2+m^2 if the field obeys the Klein-Gordon equation. But … In the end, QFT is a theory of fields and not particles. Specifically, for example, a†→p |0> creates a "particle" in a specific momentum eigenstate, and so this "particle" is not localized over any region of spacetime. So this may notion of particles is not quite in resonance with the normal notion of a particle as a corpuscular entity localized in space (to a point, or w/e).Note: The appearance of the notation for the operation above is not quite right as a copy from the thread. It's the best I can do. Superficially, these two quotes above appear to be quite contradictory. I suppose that one can resolve this apparent contradiction simply by saying that these two concepts of "particle" are related to each other by both using the word "particle". ;) 3. Since the concept of a "particle" in QM and in QFT are apparently so different, would the following be a reasonable suggestion: In order to minimize confusion and/or misunderstanding it would be useful to use different words/phrases for these two concepts, like e.g., "particle" (for QM) and "QFT particle"? If not, why not?