I have been spending some time learning about quantum groups and their representations and am interested in applications to high energy physics.
Doing a literature search I found that in the last 20 or so years people have already looked into quantum groups and the Standard Model and have used quantum groups to calculate corrections to, for example, the Gell-
Mann-Okubo mass formulas. The deformation parameter q has also been related to Cabibbo mixing.
I am wondering if anyone is aware of any as of yet unexplored applications of quantum groups to high energy physics. Perhaps with the recent experimental data that has come out over the last few years (for example Higgs data), new calculation might be possible.
In particular I would be interested at looking at some aspect where a theoretical value differs from the observed experimental value and finding out if a quantum correction could account for the difference. I am not however aware of such particular instances.
Best regards,
Niels
I working on a new structure model of particles (quarks and leptons) using coupled quantum oscillators. To moment I'm formulating only structural hypothesis that I believe should be developed through matrices with which to perform calculations on the behavior of the particles.
Dear Giovanni,
Thank you for your answer. Sounds like an interesting approach. Are you using quantum groups and/or the quantum harmonic oscillator in your work?
Niels
Dear Remi,
Thank you for your answer. I am aware that group theory is used widely in HEP. My question however is specifically about the use of quantum groups (Hopf algebras) not classical groups. I know people have replaced the groups used in HEP with their respective quantum groups. This in some cases leads to new physics or a deformation of known physics. I think this is an interesting approach.
Best regards,
Niels
Dear Niels,
one thing that is surprisingly scarcely studied in physics is the breaking of continuous to discrete groups - although discrete groups are widely used in physics, and symmetry breaking is also a key concept.
I am not sure in how far one could do something related to Hopf algebras in that respect, but for sure you can judge that aspect better. In any case, if you are interested in literature on the above topic, to give you some ideas, I can supply you witth a least a few works.
Best regards,
Alexander
Dear Alexander,
Thank you for your response and suggestion. I have not thought about the breaking of continuous to discrete groups but it seems worth looking into. If you could supply a few works that would be greatly appreciated.
Best regards,
Niels
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