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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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. / Jakobsen, Hans P.; Levichev, Alexander V.
I: Reports on Mathematical Physics, Bind 90, Nr. 1, 2022, s. 103-121.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - 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
AU - Jakobsen, Hans P.
AU - Levichev, Alexander V.
N1 - Publisher Copyright: © 2022 Polish Scientific Publishers
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - chronometric theory
KW - conformal group
KW - indecomposable representation
KW - proton-neutrino-electron
U2 - 10.1016/S0034-4877(22)00053-2
DO - 10.1016/S0034-4877(22)00053-2
M3 - Journal article
AN - SCOPUS:85138530542
VL - 90
SP - 103
EP - 121
JO - Reports on Mathematical Physics
JF - Reports on Mathematical Physics
SN - 0034-4877
IS - 1
ER -
ID: 322802843