Bound states of massless fermions

In summary, the energy of the hydrogen atom is proportional to the mass of the electron. Without a Higgs mechanism, there are no bound states of the hydrogen atom. This is general to particles with high relativistic velocities, but may have very different properties than hydrogen.
  • #1
JustinLevy
895
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 truly massless, would that prevent bound states of quarks as well? Or would there still be confinement?
 
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  • #2
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.
 
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  • #3
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?
 
  • #4
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
 

FAQ: Bound states of massless fermions

What are bound states of massless fermions?

Bound states of massless fermions refer to the phenomenon in quantum mechanics where massless particles, specifically fermions, are confined to a specific region due to the presence of a potential energy barrier. This results in the formation of a bound state, where the particles are essentially trapped and cannot escape.

How are bound states of massless fermions different from bound states of massive fermions?

The main difference between bound states of massless fermions and bound states of massive fermions is the role of mass. In the case of massless fermions, their lack of mass means they are not subject to the same conservation laws as massive particles, allowing for the formation of bound states in situations where massive fermions would not be able to form them.

What are some examples of bound states of massless fermions?

One example of bound states of massless fermions is the formation of quark-gluon plasma, where massless quarks and gluons are confined within a small region due to the strong nuclear force. Another example is the formation of excitons in certain types of semiconductors, where massless electrons and holes are bound together by their opposite charges.

What are the potential applications of bound states of massless fermions?

Bound states of massless fermions have potential applications in various fields, including condensed matter physics, high energy physics, and quantum computing. They can also help us better understand the behavior of massless particles and their interactions with the surrounding environment.

How are bound states of massless fermions relevant to our understanding of the universe?

Studying bound states of massless fermions can provide insight into the fundamental laws of physics and help us better understand the behavior of matter and energy in the universe. These bound states can also occur in extreme environments, such as black holes, providing clues about the nature of these mysterious objects.

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