This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion LCT (ILCT) and to deduce a relation between them and some properties of the elementary fermions of the Standard Model of Particle Physics. After giving the definition of ILCT for the case of a general pseudo-Euclidean space and constructing their spinorial representation, we consider the particular case of a pentadimensional space with signature (1, 4). We then deduce a classification of quarks, leptons and their antiparticles according to the values of electric charge, weak hypercharge, weak isospin and colors after the introduction of appropriate operators defined from the generators of the Clifford Algebra corresponding to the ILCT spinorial representation. It is established that the electric charge is composed of four terms, the weak hypercharge of five terms and the weak isospin of two terms. Existence of sterile neutrinos and the possibility of describing a fermions generation with a single field are suggested.
Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 6, Issue 1) |
DOI | 10.11648/j.ijamtp.20200601.11 |
Page(s) | 1-6 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2020. Published by Science Publishing Group |
Linear Canonical Transformations, Spinorial Representation, Quarks, Leptons, Standard Model
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APA Style
Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson, Wilfrid Chrysante Solofoarisina. (2020). Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation. International Journal of Applied Mathematics and Theoretical Physics, 6(1), 1-6. https://doi.org/10.11648/j.ijamtp.20200601.11
ACS Style
Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Hanitriarivo Rakotoson; Wilfrid Chrysante Solofoarisina. Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation. Int. J. Appl. Math. Theor. Phys. 2020, 6(1), 1-6. doi: 10.11648/j.ijamtp.20200601.11
AMA Style
Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson, Wilfrid Chrysante Solofoarisina. Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation. Int J Appl Math Theor Phys. 2020;6(1):1-6. doi: 10.11648/j.ijamtp.20200601.11
@article{10.11648/j.ijamtp.20200601.11, author = {Ravo Tokiniaina Ranaivoson and Raoelina Andriambololona and Hanitriarivo Rakotoson and Wilfrid Chrysante Solofoarisina}, title = {Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation}, journal = {International Journal of Applied Mathematics and Theoretical Physics}, volume = {6}, number = {1}, pages = {1-6}, doi = {10.11648/j.ijamtp.20200601.11}, url = {https://doi.org/10.11648/j.ijamtp.20200601.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20200601.11}, abstract = {This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion LCT (ILCT) and to deduce a relation between them and some properties of the elementary fermions of the Standard Model of Particle Physics. After giving the definition of ILCT for the case of a general pseudo-Euclidean space and constructing their spinorial representation, we consider the particular case of a pentadimensional space with signature (1, 4). We then deduce a classification of quarks, leptons and their antiparticles according to the values of electric charge, weak hypercharge, weak isospin and colors after the introduction of appropriate operators defined from the generators of the Clifford Algebra corresponding to the ILCT spinorial representation. It is established that the electric charge is composed of four terms, the weak hypercharge of five terms and the weak isospin of two terms. Existence of sterile neutrinos and the possibility of describing a fermions generation with a single field are suggested.}, year = {2020} }
TY - JOUR T1 - Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation AU - Ravo Tokiniaina Ranaivoson AU - Raoelina Andriambololona AU - Hanitriarivo Rakotoson AU - Wilfrid Chrysante Solofoarisina Y1 - 2020/02/26 PY - 2020 N1 - https://doi.org/10.11648/j.ijamtp.20200601.11 DO - 10.11648/j.ijamtp.20200601.11 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 1 EP - 6 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20200601.11 AB - This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion LCT (ILCT) and to deduce a relation between them and some properties of the elementary fermions of the Standard Model of Particle Physics. After giving the definition of ILCT for the case of a general pseudo-Euclidean space and constructing their spinorial representation, we consider the particular case of a pentadimensional space with signature (1, 4). We then deduce a classification of quarks, leptons and their antiparticles according to the values of electric charge, weak hypercharge, weak isospin and colors after the introduction of appropriate operators defined from the generators of the Clifford Algebra corresponding to the ILCT spinorial representation. It is established that the electric charge is composed of four terms, the weak hypercharge of five terms and the weak isospin of two terms. Existence of sterile neutrinos and the possibility of describing a fermions generation with a single field are suggested. VL - 6 IS - 1 ER -