Bound states of massless fermions

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Discussion Overview

The discussion revolves around the existence of bound states of massless fermions, particularly in the context of the hydrogen atom and quarks. Participants explore the implications of masslessness on bound states, the role of the Higgs mechanism, and related theoretical concepts such as chiral symmetry and mass gaps.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether bound states of the hydrogen atom can exist without the Higgs mechanism, suggesting that the absence of mass might lead to no bound states.
  • Another participant acknowledges the difficulty of creating bound states with massless particles, noting that such states would likely have very different properties from those of hydrogen and could be unstable.
  • Concerns are raised about the implications for quarks if they were massless, with a participant suggesting that even without a Higgs mechanism, quarks would not be exactly massless due to chiral symmetry breaking and mass gap issues.
  • A participant seeks clarification on the concept of chiral symmetry and its relevance, questioning the nature of the symmetry at different energy levels and the theoretical motivation for mass gaps in fermions.
  • Another participant asserts that chiral symmetry is spontaneously broken, referencing the absence of scalar mesons and the presence of pseudoscalar mesons as evidence.

Areas of Agreement / Disagreement

Participants express differing views on the implications of masslessness for bound states, particularly regarding the hydrogen atom and quarks. There is no consensus on the nature of chiral symmetry or the existence of mass gaps in fermions.

Contextual Notes

Participants highlight limitations in understanding the mathematics of bound states with massless particles and the complexities surrounding chiral symmetry and mass gaps, indicating that these topics are not fully resolved in the literature.

JustinLevy
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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 truly massless, would that prevent bound states of quarks as well? Or would there still be confinement?
 
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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:
Haelfix said:
even without a Higgs mechanism, you won't have exactly zero mass b/c of the chiral symmetry breaking and mass gap issues.
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?
 
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:

http://www.fuw.edu.pl/~dobaczew/maub-42w/node10.html
 

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