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I've been reading that in QFT only fields exist and a fluctuation in these fields is what we see as particles. So in this sense can we just totally disregard the notion of particles and just think of them as fluctuations of fields?

Qmechanic
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Cleo
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    Yes. Although for practical reasons, it better to see particles as particles. – Nemo Nov 11 '17 at 07:31
  • Quantum fields measure the probability of detecting a particle. If I receive a letter in the mail today with the probability of 50%, which of the two has a physical existence, the letter or the probability of me receiving it? You first must define what "exists" means. If "exists" means "observed", then quantum fields don't exist. Even if you manage to define "existence" in such a broad way that it would include mathematical abstractions as physically existing objects, particles would still remain more fundamental. – safesphere Nov 11 '17 at 18:20

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I think this is largely a matter of terminology.

The way QFT is usually taught describes the fields in terms of Fock states, and it is the excitations of these Fock states that describe the particles. Note my terminology here - I'm not saying particles are the excitations of the Fock states, I'm saying they are described by the excitations of the Fock states. The quantum field is an operator field, i.e. a mathematical object, and it's hard to see how this mathematical object can have excited states that actually are the observable particles.

But then Steven Weinberg in his QFT books starts with the particle states rather than the field i.e. exactly the opposite approach. So it's not obvious that we can claim the field is the fundamental object and the particle states only manifestations of it.

At the end of the day we can experimentally observe the objects that we call particles, and the question of precisely how we describe them mathematically seems a rather abstract one.

John Rennie
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    But the Unruh effect tells you problems with treating particles as fundamental. So prefer all fields. – AHusain Nov 11 '17 at 08:41
  • @AHusain Has the Unruh effect been observed? – safesphere Nov 11 '17 at 18:06
  • I understand that we observe particles, but is what we are observing wrong?, for example we interpret what we observe as particles but they are really just vibrations in some field? – Cleo Nov 11 '17 at 23:52
  • @safesphere Look at dumb (sound) holes. Does the case with phonon field. – AHusain Nov 12 '17 at 03:46
  • @Cleo It doesn't matter what label you put on them. The point is that we observe consistent objects with well defined and stable parameters. For example, all electrons are identical from the standpoint that they have the same mass, 1/2 spin, electric charge, electron/lepton charge. "Particles" doesn't mean "little balls", this is not the point. The point is that we never observe a "half of an electron" or "0.1 of an electron" or "1.5". It is always one or, if more, then a whole number of them. You are free to think of them as "field vibrations", but this "field" has not been observed. [...] – safesphere Nov 12 '17 at 03:56
  • @Cleo Furthermore, quantum fields are not observable in their very nature, because they predict the probability of observing a particle. For example, if you roll dice and calculate the probability of a particular outcome, then, no matter how carefully you observe, you would never see "the probability" as a physical object. What you would see is the physical dice in a particular configuration. So again, you can label particles "excitations of the field", but it would not change the fact that, if exist=observed, then particles (or "excitations" if you will) exist, but quantum fields do not. – safesphere Nov 12 '17 at 04:04
  • @safesphere, so to be clear then, particles and field vibrations are essentially describing one thing that is what you said "observe consistent objects with well defined and stable parameters", so you can't really dismiss either term. – Cleo Nov 13 '17 at 01:45
  • Particles clearly obey what the fields tell them to do, but "reluctantly", in a random order. So in some peculiar sense the fields are "real" and must "exist" somehow somewhere, on a different plane of existence from us. It's like there is a separate reality of mathematical abstractions on top of and in charge of our physical reality. No one knows how this works. Experimentalists observe particles. Mathematicians worship quantum fields and denounce physical reality. This is why there are over 20 interpretations of quantum mechanics. A giant computer simulation could be a possible explanation. – safesphere Nov 13 '17 at 05:35
  • In what way do we observe particles as such. In terms of them being little hard lumps, I mean. If not that, it is not really a particle. – Ponder Stibbons Oct 21 '22 at 06:28
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To answer the question directly, yes. I disagree with John's answer: Fields are certainly fundamental in QFT - Weinberg starts from history and the reader's scattering intuition from QM but his volumes are definitely based on fields. In some cases it is downright incorrect to speak of particles so the distinction is important.

A particle describes the phenomenon of a quantum field excitation where the underlying mathematical structure is that of real/complex/spinor valued field over some spacetime manifold. In Weinberg, there is a discussion of little groups which I think very elegantly connects the two notions: Particle states are labeled by their little group representations. The quantum mechanical spin for instance can be thought of as little group SU(2) associated with the rotational invariance in a particular frame. So the particle state would be labeled by the momentum in the frame and the representation of SU(2) which come in half integers. This is one way one would think about energy and spin quantum numbers from a QFT perspective.

Usually it is okay to think phenomenologically - a local excitation of the Dirac field can be thought of as a particle, sure. What if I have a strongly interacting theory? What if I have collective excitations? What if I want to talk about non-local operators? The particle intuition will fail you the deeper you delve into the subtleties of QFT. One might argue that this intuition is a valuable learning tool, especially coming out of QM but you should think of it as training wheels and do away with them ASAP if you are interested in high energy theory.

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