A representation of SU(2, 2) which can be interpreted as describing chronometric fermions (proton, neutrino, and electron) in terms of a single composition series
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In 1991 I. E. Segal stated (on the basis of a certain induced representation of the conformal group, but without proof) that there are four chronometric elementary particles of spin 1/2. In terms of the same representation (but using a different parallelization), we discuss a model where there are just three of those particles. They are interpreted as the proton, the (electronic) neutrino, and the electron, respectively. Mathematically, the three particles correspond to factors of the composition series. Each of the three representation spaces (Fp, Fv, and Fe, respectively) is provided with an invariant unitary structure and, in each of the three cases, energy positivity holds. These findings may shed some light on why there are lepton generations at all. The conclusions are mathematically based on the specific formula for the action of our representation in the full representation space F. This formula is presented in terms of the so-called reproducing kernel functions which are related to coherent states.
Originalsprog | Engelsk |
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Tidsskrift | Reports on Mathematical Physics |
Vol/bind | 90 |
Udgave nummer | 1 |
Sider (fra-til) | 103-121 |
ISSN | 0034-4877 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
The research by A. V. Levichev was partially supported by the Program of fundamental scientific research of the SB RAS No. I.1.2., project No. 0314-2019-0006.
Publisher Copyright:
© 2022 Polish Scientific Publishers
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