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Bound states of massless fermions

  1. Feb 8, 2009 #1
    If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that I see no bound states when I let the mass -> 0?)

    Second question, if there aren't bound states for that reason, how general is this? For example, if the quarks were truely massless, would that prevent bound states of quarks as well? Or would there still be confinement?
  2. jcsd
  3. Feb 9, 2009 #2


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    It would certainly be a challenge to create a bound state with a massless particle. The mathematics of Bound states with highly relativistic particles is difficult and controversial and I don't believe there is agreement in the literature. Certainly it would have very different properties than hydrogen and would be highly unstable.

    As for the quarks, well yea in reality even without a Higgs mechanism, you won't have exactly zero mass b/c of the chiral symmetry breaking and mass gap issues. But since the mass scales are completely different you'd have again, very different physics than you are used too.
    Last edited: Feb 9, 2009
  4. Feb 9, 2009 #3
    I'm not sure what you are referring to here, would you mind explaining a bit more to help me understand?

    By chiral, do you mean left/right handed? I thought that was not a good symmetry at any energy (ie. it is not a spontaneously broken symmetry). As for mass gap, I've never really understood what motivates that expectation theoretically. Bosons don't necessarily have a mass gap, why should the fermions?
  5. Feb 9, 2009 #4


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    It is a spontaneous broken symmetry since you only have pseudoscalar mesons in nature, and no real scalar ones (i.e no positive parity partners for e.g. the pions)

    This is a quite good (maybe a bit too technical) article about this:

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