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Empirical success of non-pert methods in QFT?

  1. Oct 18, 2011 #1
    Someone said at a conference today that there was no empirical support whatsoever for the idea that non-perturbative methods could be successfully applied in QFT. Does anyone know any counterexamples to this claim? I don't work in this area, but it sure doesn't sound right to me...

    Any info gratefully received!
  2. jcsd
  3. Oct 18, 2011 #2


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    In low-energy QCD both analytical and numerical results are obtained via np-methods for mechanisms of confinement, chiral symmetry breaking and hadron mass generation. The biggest success is the application of lattice QCD to hadron spectroscopy with afaik approx. 5% error for hadron masses.

    Strictly speaking low-energy effective theories like chiral perturbation theory, heavy baryons etc. are not np-methods as these models are not derived explicitly via integrating out high-energy d.o.f. but in a wider sense they are something like np-methods as well. In 1+1 dim. theories such methods ca be related to the full theory rigorously.
    Last edited: Oct 18, 2011
  4. Oct 18, 2011 #3


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    Yes, that's complete nonsense, depending of course on what he meant exactly.

    Instanton's are the analogue of tunneling effects in quantum mechanics, which is of course well tested. They are ubiqitous in the study of anomalies, as well as in QCD and other areas of particle physics. A good example would be the physics of the Eta prime particle, which Witten solved using nonperturbative physics.

    There are many examples of experimentally verified solitons in condensed matter physics.

    As far as other nonperturbative techniques. Well, in some sense the Dyson gas technique is known to be correct in describing 2 dimensional plasmas.
  5. Oct 19, 2011 #4


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    Very good examples, especially the relation anomaly - instanton - eta-prime mass; for the latter only the anomay and therefore only a non-perturbative method can provide an explanation

    (many people think that the anomaly is purely perturbative due to the triangle in one loop; this is completely nonsense; it's like saying that every blue paint is heaven b/c the color of heaven is blue)
    Last edited: Oct 19, 2011
  6. Oct 19, 2011 #5


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    The whole treatment of symmetry broken states is non-perturbative to start with.
  7. Oct 19, 2011 #6


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    yes, but in many cases it's a classical ground state around which one uses standard perturbation theory
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