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No Particles in QCD?

  1. Sep 30, 2006 #1


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    CarlB called attention to this paper by Johan Hanssen: http://arxiv.org/abs/hep-ph/0011060, on the BTSM forum. Hanssen asserts that because the Lagrangian of QCD is nonlinear, since the structure constants for su(3) do not vanish, therefore you can't do Fourier transforms on the fields, and hence can't define the ladder or number operators, so no particles, only interacting fields. He uses this to show why quarks cannot exist in isoloation (the supposed quark in the source of a color field, which, by nonlinearity is also itself the source of a color field, ... Thus the quark is always a nexus of intracting fields and cannot be isolated.

    What does anybody here think of this line of argument?
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  3. Oct 1, 2006 #2


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    The problem is that it is an argument, not a proof. But of course this kind of argumentation, "no particles", has been around QCD since its origins.
  4. Oct 1, 2006 #3


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    Well, then, what is the state of play? Do people actually use the creation/deletion operators in spite of the Fourier transform being undefined due to the curvature of the SU(3) group manifold? Or is the allegation that it is undefined a false one? Is this a pertubative issue? What do the phenomenologists, who cling to their observational partons in spite of all the Nobels for QCD, think about it?
  5. Oct 1, 2006 #4


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    Another paper by the same author gives another facet to the argument:

    The "proton spin crisis" - a quantum query
    Yohan Hansson, (2003)
    The "proton spin crisis" was introduced in the late 1980s, when the EMC-experiment revealed that little or nothing of a proton's spin seemed to be carried by its quarks. The main objective of this paper is to point out that it is wrong to assume that the proton spin, measured by completely different experimental setups, should be the same in all circumstances.

    This reminds me of something I read in Landau and Lif$hitz (probably QM or just maybe RQM) some time ago, to the effect that the usual rules for adding angular momentum only work in a weak interaction regime. I'd never read anything like that before and it stood out to me. It was only a footnote and they didn't explain more.

    Last edited: Oct 1, 2006
  6. Oct 2, 2006 #5
    I don't think this is a valid criticism of QCD. It is true that one normally applies the boundary condition of vanishing fields at infinity, but I can't see any reason why one couldn't put in an infra-red cut-off and still make fourier decompositions. Of course, then your theory becomes an approximation, but in perturbation theory we are making approximations anyway, and at high energies where we have asymptotic freedom it will be a very good approximation. After all, the factorization of different energy scales is well know.

    But the proof of the pudding is in the eating. QCD makes predictions, and these predictions are well verified by experiment.

    One can of course object to the use of the word particle, but I would contend that you are using a rather specific definition of the word. After all, no system is ever truely asymptotically free.
  7. Oct 2, 2006 #6


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    That's no excuse for doing things you know to be wrong. The predictions of QED are even more accurate, and many think that QED "doesn't even exist" as a well-defined theory (Landau pole, e.g.).

    A map representing a limited area on Earth as flat is pretty accurate too, but doesn't justify saying the world is flat.
  8. Oct 2, 2006 #7
    Sure it does. No-one thinks QED or QCD exist in a vacuum (no pun intended). They are part of a grander theory, so the QED Landau pole problem is not really a problem (since other physics will be applicable at that scale) and similarly the QCD asymptotic states problem is not a problem either.

    The final theory of everything had better be well definied, since it has no new physics to fall back on, but that is another issue.
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