What are the fields that exist in the standard model and QFT? I know the electromagnetic field and the Higgs field, but what other fields are there? Also, how do they interact?

  • $\begingroup$ I removed the unrelated content, thanks. $\endgroup$ – sakurashinken Dec 29 '20 at 18:46

By one way of counting there are 17 fields in the Standard Model:

  • 6 for quarks (up, down, strange, charm, top, bottom)
  • 3 for charged leptons (electron, muon, tau)
  • 3 for neutrinos (electron neutrino, muon neutrino, tau neutrino)
  • 1 for photon (carrier of electromagnetic force)
  • 1 for gluon (carrier of strong nuclear force)
  • 1 for W weak boson (charged carrier of weak nuclear force)
  • 1 for Z weak boson (neutral carrier of weak nuclear force)
  • 1 for Higgs

In this way of counting, a field describes both a particle and its antiparticle, and a single field (such as an up quark field or a gluon field) can have multiple “color charges” for the strong nuclear force. If you count all of these as separate fields you get 61 instead of 17.

This Wikipedia diagram shows their interactions.

Each field fills all of space. All electrons in the universe, for example, are quanta of a single electron field pervading the universe, and the same is true for any other kind of elementary particle.

Different kinds of fields cannot superpose with each other; they simply coexist at every point and interact in various ways. Some fields, such as gluons, do not simply superpose even with themselves, because they have nonlinear self-interactions.

There are an infinite number of possible fields and interactions that a quantum field theory can consider. The Standard Model is one very specific quantum field theory that seems to do an excellent job of describing nature at the energy scales we can test.

  • $\begingroup$ And how then would we view empty space? As a superpositions of these fields? $\endgroup$ – sakurashinken Dec 29 '20 at 18:44
  • $\begingroup$ “Empty” space means the vacuum state of this theory, where each field is in its lowest-energy state with no quanta. (Think of a quantum harmonic oscillator in its ground state.) However, since the fields interact the vacuum state is not as trivial as it sounds. $\endgroup$ – G. Smith Dec 29 '20 at 19:19
  • $\begingroup$ To highlight the underlying simplicity of the standard model, we normally count things a little differently: instead of counting $W$ and $Z$ and electromagnetism as three fields, we can count them as two fields: one $U(1)$ gauge field that couples asymmetrically to the left- and right-handed chiral components of the fermion fields, and one $SU(2)$ gauge field that couples only to the left-handed chiral components of the fermion fields. These two fields are mixed with each other by their coupling to the Higgs field, resulting in what we experience as $W$ and $Z$ and electromagnetism. $\endgroup$ – Chiral Anomaly Dec 29 '20 at 22:15
  • $\begingroup$ It's also important to realise that these are operator-valued fields, so to say that "a photon is an wave in the photon field, rippling through spacetime" is not strictly correct. $\endgroup$ – Nihar Karve Dec 30 '20 at 2:58

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