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Reading Student Friendly Quantum Field Theory by Robert Klauber and he made me realize I've taken as fact for some time that bosons are the "force carriers" in QFT, without really understanding fully why that's the case. Anyhow, it is this passage from the text that got me wondering:

"The advent of the Pauli Exclusion, with the realization that fermions and bosons differ, led to the understanding that many bosons could coalesce into a macroscopic classical field"

Okay, that makes sense for a classical field, I suppose. But, what does this mean in QFT, especially in light of the fact that the bosons found in Feynman Diagrams are virtual particles that are un-detectable, even in principle? How exactly does the phrase "bosons could coalesce" transfer over here? Also, a couple example of spin 1/2 fields are spinors representing electrons and positrons, correct? These are fermions, not bosons, which the field operator are representing, correct? Seems like fermions play some role? You often hear the explanation that electrons are just manifestations of the electron field

The Pauli Exclusion Principle applied to the atom and orbitals and why we have chemistry makes a lot of sense. The way it was applied to fields here seems a bit more nebulous, I guess.

Sounds to me like fields can be composed of either fermions or bosons, but for the experimenter to be able to interact with the field, it must be a force-producing field, which can only happen with bosons. Again, the Pauli Exclusion Principle here seems a bit more nebulous to me at this point.

Anyhow, these are some of the questions that popped into my mind. Any feedback on these are any extra insights that can add elucidation here would be appreciated.

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  • $\begingroup$ Keep in mind that virtual particles are feynman's way of perturbation. The only physical part is the external lines, but we're used to do perturbation so we add a bunch of virtual particles(for the sack of Lorenz invariance), and that contains not only bosons, but also fermions. As for your question about four fundamental interactions, I think? Or maybe yukawa included, just try Compton scattering. $\endgroup$
    – Turgon
    Apr 2, 2017 at 0:43
  • $\begingroup$ The important word here is macroscopic "classical" field. Bosonic fields can coalesce and form a classical non-zero background, like the non-zero Higgs vev. There is no analogous fermionic field background, or for instance, classical fermionic waves. $\endgroup$
    – Prahar
    Apr 2, 2017 at 3:33

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Usually the particles that are exchanged between matter particles are fundamental bosons. This is because they lack lepton number and baryon number. There are it turns out some bosons that have fermions in them(like the pions). The difference between a boson and a fermion comes mostly from their spins. A fermion has a fractional spin of anything than can be divided by 1/2 times Planck's constant. Or just 1/2 of spin. Bosons have integer spins. Of course fermions follow Pauli exclusion principle as you say.

Even a Helium-4 nucleus is a boson however it is not a force carrier.

As I said earlier most force carriers are fundamental bosons and sometimes pions.

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