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.

In: Reports on Mathematical Physics, Vol. 90, No. 1, 2022, p. 103-121.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Jakobsen, HP & Levichev, AV 2022, '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', Reports on Mathematical Physics, vol. 90, no. 1, pp. 103-121. https://doi.org/10.1016/S0034-4877(22)00053-2

APA

Jakobsen, H. P., & Levichev, A. V. (2022). 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. Reports on Mathematical Physics, 90(1), 103-121. https://doi.org/10.1016/S0034-4877(22)00053-2

Vancouver

Jakobsen HP, Levichev AV. 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. Reports on Mathematical Physics. 2022;90(1):103-121. https://doi.org/10.1016/S0034-4877(22)00053-2

Author

Jakobsen, Hans P. ; Levichev, Alexander V. / 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. In: Reports on Mathematical Physics. 2022 ; Vol. 90, No. 1. pp. 103-121.

Bibtex

@article{dd73b57c6609497692d7111e94a60142,
title = "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",
abstract = "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.",
keywords = "chronometric theory, conformal group, indecomposable representation, proton-neutrino-electron",
author = "Jakobsen, {Hans P.} and Levichev, {Alexander V.}",
note = "Publisher Copyright: {\textcopyright} 2022 Polish Scientific Publishers",
year = "2022",
doi = "10.1016/S0034-4877(22)00053-2",
language = "English",
volume = "90",
pages = "103--121",
journal = "Reports on Mathematical Physics",
issn = "0034-4877",
publisher = "Pergamon Press",
number = "1",

}

RIS

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