It appears to me that in Quantum field theory (QFT), particles ( such as electrons, quarks, W and Z mesons, and possibly neutrinos) are considered to be fields. This is a difficult concept to get. A field as one usually conceives of it is a region of spacetime that is continous and its physical properties vary from point to point. (Example: Electromagnetic field and Gravitational field). In QFT, we are transcending the particle concept and possibly the wave packet picture. For example, the electron in the hydrogen atom is not like a little point moving arround the nucleus, nor is it a cloud of probability density. It is a physical field. This then leads to the physical collapse of the electron field when it deposits its energy as a quantum. Field collapse becomes real. But, how do we visualize this electron field? This gets worse when we consider that the electron has "spin" which is really intrinsic angular momentum. Then, does this all mean that "electron spin" is in itself another type of field?
My answer to the spin question is yes. No answer yet for the visualizing question.
Electron fields are fermionic fields. In general, these fermion fields can be considered as a superposition of the vacuum state |0> and the state "an electronis there" |1>. One has the electron state
|e> = a|0> + b|1>, a²+b²=1 (Normalization)
and the b gives us the amplitude of the electron being present. b² is then the corresponding probability. One may visualize the electron field with a region that can be coloured black or white. The more the value a (vacuum), the more white is the region. And more black means more electron presence probability; in the special case that b(x) = 1 on a point of spacetime x, the region around x can be complitely painted black. In the case that neither a nor b is 1 at some point x, the region around this point can be visualized as follows:
White dots are mixed randomly between the "black ink", such that the nature of vacuum fluctuations is depicted. Looks then like the black-white blurred background known from old TVs (when no program is selected).
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