I studied QED and QCD and I know that there is an vacuum state for each theory $|{0}\rangle_{QED}, |{0}\rangle_{QCD}$ where we describe the particles as excitations of that vacuum state. But can we also say that this state is our quantum field and further is there one single vacuum state for the Standardmodel theory?

In other words: Does it makes sense if we talk about the one and only quantum field and all interactions and particle creations and anihilations are only excitations of this field?

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    $\begingroup$ If you studied QED/QCD you should know that there is more than one field (quantum or not) in those theories. The vacuum state is wholly different from being a field and I'm puzzled why you would try to say that this state "is our quantum field". $\endgroup$
    – ACuriousMind
    Apr 15 '17 at 14:49
  • $\begingroup$ @ACuriousMind You can $\oplus$ together all the fields to treat them as one big field. Also, there's only one vacuum state rather than one for each field. Maybe that's what StrangeField is saying? $\endgroup$ Apr 15 '17 at 15:59
  • $\begingroup$ I shouldn't better wrote something else as "the one quantum field" of course there are many fields. The question was more of the kind: Can I say that all fields causes excitations (particles) of something (not sure if this is our ground state)? $\endgroup$ Apr 15 '17 at 18:39
  1. Quantum field theory just reflects our current understanding of the universe, which continuous to develop as time goes. We already know that the Standard Model is not the ultimate description of our universe. For example, quantum gravity is not included in the Standard Model. So even if we can unify QED and QCD and everything in the Standard Model into a Grand Unified Theory, it is still not the ultimate quantum field that can describe everything (although it can describe pretty much a lot of things we have known). As our knowledge of the universe increases, new quantum fields may be introduced (such as supersymmetry fields) or we may even go beyond quantum field theory (such as the string theory). If you believe that we can never know the ultimate truth of the universe, then we should not be obsessed with the idea of THE quantum field.

  2. The vacuum state of a quantum field theory (QFT) is not unique. Even if we are given a well-formulated QFT, its ground state (or its vacuum state) is not unique. A QFT typically has infinitely many vacuum states related by symmetry or by large gauge transformations. We do not even know which vacuum state we are living in currently. There is no local detection/measurement to tell the different vacuum states apart.


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