From an author who is also a professor emeritus (does it matter where?):
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https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf
I note this guy says the Schroedinger eqn is a field eqn. That makes sense if it defines a field.
Let's look in a bit more detail about what that guys says, shall we?
A benefit of QFTs is that quanta of a given field must be identical because they are all excitations of the same field, somewhat as two ripples on the same pond are in many ways identical.
Note: quanta are like ripples in a pond. They are not the pond. They are the ripples.
When a field changes its energy by a single quantum, it must do so instantaneously, because a non-instantaneous change would imply that, partway through the change, the field had gained or lost only a fraction of a quantum. Such fractions are not allowed because energy is quantized. Field quanta have an all-or-nothing quality.
Unfortunately, for the uninitiated, it is possible to get the impression that the
energy quanta he is talking about here are the same thing as the
field quanta. They are not the same thing. The first two sentences talk about what happens to the energy associated with the field. The last sentence talks about the excitations of the field itself, which are a different thing.
The QFT language of creation and annihilation of quanta expresses this nicely. A quantum is a unified entity even though its energy might be spread out over light years--a feature that raises issues of nonlocality intrinsic to the quantum puzzle.
Here, he talks about the
field quanta again, not
energy quanta.
"Fields are all there is" should be understood literally. For example, it's a common misconception to imagine a tiny particle imbedded somewhere in the Schroedinger field. There is no particle. An electron is its field.
An electron is its field, in the sense that it is an excitation of a field. The electron is a ripple in the pond that is the electron field.
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The take-away message here, for the purposes of this thread, is that, once again, nothing here says that field quanta are energy, or that energy quanta are the same thing as field quanta, or that particles are energy, or any of that rubbish.