>>16705893It's not total bs in the following sense. In perturbation theory (just general QM, not specific to QFT), you get the leading-order correction
[eqn]E_n^{(1)} = \langle \psi_n | V | \psi_n \rangle[/eqn]
The next order term is
[eqn]\sum_{m\not=k}\frac{|\langle \psi_n | V| \rangle \psi_m \rangle|^2}{E_n^{(0)}-E_m^{(0)}}[/eqn]
Notice the sum. You have to sum over ALL states in the Hilbert space, regardless of what they are. When you do the next order, you get two sums and so on.
This is a consequence of using the completeness property of the Hilbert space to derive the perturbative corrections. It's something that shows up because we want to do perturbative theory and for no other reason.
Now, when you move on to more complicated examples of the same idea, you get the Born series, the Lippmann-Schwinger equation, the Dyson series and so on. But the idea remains the same: whenever you go to higher-than-leading order of corrections, you end up summing over states.
Now in QFT we interpret states as particles (via Fock spaces). So in this technique, we are "summing over all possible particle states" even though those particles are "virtual" and "off-shell". This is often mystified by saying le quantum woo produces particles out of thin air because muh weird quantum mechanics. No, you're literally just doing an approximation and your approximation technique has you make these expansions. There's absolutely nothing "weird" about this, because it's you doing these approximations, not Nature. Nature doesn't even know what perturbation theory is.