English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper is a continuation of our works concerning Linear CanonicalTransformations (LCT) and Phase Space Representation of Quantum Theory. Thepurpose is to study the spinorial representation of some particular LCT calledIsodispersion LCT (ILCT) and to deduce a relation between them and theelementary fermions of the Standard Model of Particle Physics. After giving thedefinition of ILCT for the case of a general pseudo-Euclidean space andconstructing their spinorial representation, we consider the particular case ofa pentadimensional space with signature (1, 4). We then deduce a classificationof quarks, leptons and their antiparticles according to the values of electriccharge, weak hypercharge, weak isospin and colors after the introduction ofappropriate operators defined from the generators of the Clifford Algebracorresponding to the ILCT spinorial representation. It is established that theelectric charge is the sum of four terms, the weak hypercharge of five termsand the weak isospin of two terms.Existence of sterile neutrinos is suggestedand the possibility of describing a fermions generation with a single field isdiscussed.

Properties of Elementary Fermions of the Standard Model deduced from Linear Canonical Transformations