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I've read many things about particles "swimming" in a quantum field, but what exactly does this mean? At the quantum level, I understand that a particle (like a quark and perhaps even further down to a string) is really just a vibrating wave form. So does this mean that when a particle interacts with a quantum field, it is really setting the zero-energy of the field to vibrating, which then becomes non-zero?

Would an example be a wire with no electricity flowing as a zero energy field? When we apply a current, the electrons move and become non-zero. Could we describe the wire as a field?

Qmechanic
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foolishmuse
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    All particles are the quanta of various quantum fields, and it is really always fields that are interacting with fields. – G. Smith Feb 28 '20 at 16:56
  • I'm not sure about "swimming." Don't try to take this analogy very far, but it might be a little bit closer to the truth if you to think of a particle as a "thing" in a field in the same way that a knot is a "thing" in a piece of rope. – Solomon Slow Mar 18 '20 at 17:14

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QFT (quantum field theory) can be regarded as quantum mechanics with an infinite number of harmonic oscillators. Particles are described as excitations (quanta) of the quantum fields, which are more fundamental than the particles.

Interactions between particles are described by interaction terms in the Lagrangian constructed with the corresponding fields. Each interaction can be pictorially represented by Feynman diagrams according to the perturbative expansion of the transition amplitude from initial to final states.

Note:
Your allegory is not proper, as the electricity flowing in the wire is confusing. An excited state of a quantum field can be simply imagined as a vibrating string, as the harmonic oscillator model would suggest.

Michele Grosso
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I'll give my experimental particle physicist view which is differing from Michele's only in words, not in mathematics.

As he says field theory is a higher model based on quantum mechanics and its postulates. One can have a field theory on other quantum entities than on particles, as I learned back in 1961, when I was taught a model where nuclear reactions were described by a field theory.

Let us take the electron field postulated by QFT as existing in every point in space time. It is modeled by the plane wave solution of the Dirac equation for electrons. ( correspondingly for each particle in the table, its appropriate equation and solutions). It is like a Lorentz invariant aether where creation and annihilation operators can move particles along.

Actually for real particles a wavepacket solution is needed to model it, as plane waves give uniform probabilities for the particle to exist up to infinity. Thus if we wanted to describe a real electron track, a spread in energies commensurate with the Heisenberg uncertainty for that momentum would be used. In the formulation of the Feynman diagrams this is not needed, as it is only the interactions that are necessary for calculating crossections and decay probabilities.

How does a particle interact with a quantum field? So a particle is described by a quantum field, and creation and annihilation operators. It does not interact with the field, it interacts with other particles' quantum fields, as seen pictorially in the Feynman diagrams drawings. It is the combination of fields and creation and annihilation operators that define the interactions between different particles.

I would like to stress also that the waves in quantum mechanics are probability waves, how probable it is to find a particle at an x, y,z. Not distribution of energy and mass in space. This is clearly seen in the double slit experiment one electron at a time.

anna v
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