Volume 6, Issue 1, March 2020, Page: 1-6
Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation
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
Received: Jan. 30, 2020;       Accepted: Feb. 14, 2020;       Published: Feb. 26, 2020
DOI: 10.11648/j.ijamtp.20200601.11      View  180      Downloads  78
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.
Keywords
Linear Canonical Transformations, Spinorial Representation, Quarks, Leptons, Standard Model
To cite this article
Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson, Wilfrid Chrysante Solofoarisina, Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation, International Journal of Applied Mathematics and Theoretical Physics. Vol. 6, No. 1, 2020, pp. 1-6. doi: 10.11648/j.ijamtp.20200601.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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