Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation

Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Hanitriarivo Rakotoson; Wilfrid Chrysante Solofoarisina

doi:doi:10.11648/j.ijamtp.20200601.11

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Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson, Wilfrid Chrysante Solofoarisina

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 6, Issue 1)

Received: 30 January 2020 Accepted: 14 February 2020 Published: 26 February 2020

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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.

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
Creative Commons	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.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Linear Canonical Transformations, Spinorial Representation, Quarks, Leptons, Standard Model

References

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[2]	Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Rakotoson Hanitriarivo, Victor Harison, Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators, arXiv: 1401.6526 [quant-ph], International Journal of Latest Research in Science and Technology ISSN (Online): 2278-5299, Vol. 3, Issue 1, pp. 48-52, January-February 2014.
[3]	Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Rakotoson Hanitriarivo, Wilfrid Chrysante Solofoarisina: Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics, arXiv: 1503.02449 [quant-ph], International Journal of Applied Mathematics and Theoretical Physics. Vol. 1, No. 1, pp. 1-8, 2015.
[4]	Hanitriarivo Rakotoson, Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Raboanary Roland, coordinate, momentum and dispersion operators in phase space representation, arXiv: 1707.02223 [quant-ph], International Journal of Latest Research in Science and Technology, ISSN (Online): 2278-5299 Vol. 6, Issue 4, pp. 8-13, July-August 2017.
[5]	Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson, Hasimbola Damo Emile Randriamisy, Dispersion Operators Algebra and Linear Canonical Transformations, arXiv: 1608.02268 [quant-ph], International Journal of Theoretical Physics, Vol. 56, Issue 4, pp. 1258–1273, Springer, April 2017.
[6]	Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson, Study on a Spinorial Representation of Linear Canonical Transformation, arXiv: 1711.04975 [quant-ph], International Journal of Applied Mathematics and Theoretical Physics. Vol. 5, No. 3,, pp. 58-65, 2019.
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[8]	Hanitriarivo Rakotoson, Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Roland Raboanary, Linear Canonical Transformations in Relativistic Quantum Physics, arXiv: 1804.10053 [quant-ph], 2018.
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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

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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

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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

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@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}
}

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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  -

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Author Information

Ravo Tokiniaina Ranaivoson

Information Technology and Theoretical Physics Department, National Institute for Nuclear Science and Technology (INSTN-Madagascar), Antananarivo, Madagascar
Raoelina Andriambololona

Information Technology and Theoretical Physics Department, National Institute for Nuclear Science and Technology (INSTN-Madagascar), Antananarivo, Madagascar
Hanitriarivo Rakotoson

Information Technology and Theoretical Physics Department, National Institute for Nuclear Science and Technology (INSTN-Madagascar), Antananarivo, Madagascar
Wilfrid Chrysante Solofoarisina

Information Technology and Theoretical Physics Department, National Institute for Nuclear Science and Technology (INSTN-Madagascar), Antananarivo, Madagascar

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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

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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

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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

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@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}
}

Copy | Download

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  -

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