Question on particles/fields in QFT

[AuraCrystal]

Hello,

I've been reading a book on QFT (specifically, Atchison and Hey) and they say that a classical field can be expanded into an integral of harmonic oscillators. When you quantize the scalar field $\phi$, it becomes an operator. Now, this is an infinite number of quantum oscillators. Do these correspond to particles? Of course, you can also write out the Hamiltonian in this way; in other words, does the energy of the field equal the sum of all the energies of these particles?

 

[Matterwave]

Yes, basically. 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 (they will obey this relation if the field obeys the Klein-Gordon equation). But be careful with the notion of particles in QFT. In the end, QFT is a theory of fields and not particles.

Specifically, for example, $a^\dagger_\vec{p}|0\rangle$ 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).

 

[AuraCrystal]

OK, so is it the modes in the Fourier expansion of phi or is it the quantum of the excitation that is the particle?

 

[AuraCrystal]

Never mind, I just misread something in the book. ^_^; I think I get it now; the energy of the field comes in discrete "packets" which can be interpreted as particle, but at the end of the day, all they really are (from the standpoint of QFT) is "packets" of the field.

(Also, sorry for the double post. It won't let me edit my other one.)