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Confusion (7) from Weinberg's QFT.(Why is there a vacuum field)

  1. Sep 1, 2011 #1
    According to Weinberg's logic, quantum fields are just convenient building blocks of constructing a Hamiltonian which can give a lorentz invariant S-matrix, then why must we consider vacuum filled with quantum fields and say there's no true vacuum since there's always fluctuations of quantum fields? After all, if all we want is the final Hamiltonian which gives a lorentz invariant S-matrix, why should we treat the field as a realistic entity on its own?
     
  2. jcsd
  3. Sep 1, 2011 #2
    To what extent you regard quantum fields as "realistic" is up to you. Quantum field theory is the basis for theories like Quantum Electrodynamics or the Standard Model, which describe experiments quite well. Therefore the concept of fields is a good one.
    The S-Matrix describes dynamical interaction between those fields and lets one calculate physical quantities.
     
  4. Sep 1, 2011 #3
    I think that in the spirit of Weinberg's book one can reasonably make an argument that particles are the true constituents of nature and that quantum fields are just abstract mathematical quantities, which are needed only for construction of interaction terms in the particle Hamiltonian.

    Eugene.
     
  5. Sep 1, 2011 #4
    Yes, then I wonder does it still make sense to talk about vacuum fluctuation etc.? Since there might not be a underlying quantum field?
     
  6. Sep 1, 2011 #5
    There is no sense to talk about quantum fluctuations, because nobody has ever measured them directly.

    Eugene.
     
  7. Sep 2, 2011 #6

    vanhees71

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    You need the vacuum state to build a proper Fock space. "Quantum fluctuations" are a perturbative notion, i.e., one starts with non-interacting particles/fields and then treats the interaction perturbatively (or uses perturbation theory as a starting point for more sophisticated approximations like resummations of diagram classes like Hartree-Fock, RPA, etc.).

    Roughly speaking, every perturbative Feynman diagram with no loops ("tree-level diagrams") describe the non-quantum (classical) approximation of the physical processes, taking place in the perturbative vacuum. Any loop correction takes into account quantum effects and thus are called "quantum fluctuations". These have measurable consequences like the Lamb shift of atomic spectral lines, the Casimir effect, etc. and are thus established empirical facts at a high level of accuracy.
     
  8. Sep 2, 2011 #7
    Well, the term "quantum fluctuation" refers to a misleading interpretation of loop corrections. It implies that there are virtual particles appearing and disappearing, contributing to the energy of the fields. There is no evidence that this is actually happening. Loop corrections however are just a mathematical part of the theory that need to be taken into account because the theory demands it. There's no need in giving those correction terms additional physical interpretation.
     
    Last edited: Sep 2, 2011
  9. Sep 2, 2011 #8

    vanhees71

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    That's true. To talk about "virtual particles" is just a convenient jargon to talk about abstract mathematical expressions of perturbation theory. Nevertheless they have observable consequences and lead to the most accurate consistency between theory in experiments in physics (e.g., the anomalous magnetic moment of the electron is predicted by QED to around 12 or more significant decimal digits!).
     
  10. Sep 2, 2011 #9
    Then I can argue vacuum state may not be true vacuum, if there's no convincing reason to believe there's a underlying quantum field, I may just as well imagine a pure void as the true vacuum.
     
  11. Sep 2, 2011 #10
    By the way does Casmir effect prove the existence of zero-point energy? so is it a evidence of a underlying quantum field?
     
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