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

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

doi:10.11648/j.ijamtp.20200601.11

Cited by 2 publications

(4 citation statements)

References 2 publications

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“…Like in [26] we define Isodispersion Linear Canonical Transformations (ILCTs) as the LCTs fulfilling the relation…”

Section: -Transformations Laws Of Reduced Operators and Ilctsmentioning

confidence: 99%

“…Like in [26], we may define Isodispersion LCTs (ILCTs) as the LCTs which leaves invariant the quantity †…”

Section: -Phase Space Representation and Lcts Properties In Multidime...mentioning

confidence: 99%

“…As it is well known, the current formulation of relativistic quantum theory use a four dimension pseudo-Euclidian space with signature (1,3). But according to our work [26], it may be interesting to investigate the case of space with higher dimension. Anyway, the formalism developed through this work can be applied for any case of pseudo-Euclidian space.…”

Section: -Conclusionmentioning

confidence: 99%

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Linear Canonical Transformations in relativistic quantum physics

Ranaivoson¹,

Andriambololona²,

Rakotoson

et al. 2021

Phys. Scr.

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Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the canonical commutation relations characterizing the coordinates and momenta operators. In this work, the possibility of considering LCTs to be the elements of a symmetry group for relativistic quantum physics is studied using the principle of covariance. It is established that Lorentz transformations and multidimensional Fourier transforms are particular cases of LCTs and some of the main symmetry groups currently considered in relativistic theories can be obtained from the contractions of LCTs groups. It is also shown that a link can be established between a spinorial representation of LCTs and some properties of elementary fermions. This link leads to a classification which suggests the existence of sterile neutrinos and the possibility of describing a generation of fermions with a single field. Some possible applications of the obtained results are discussed. These results may, in particular, help in the establishment of a unified theory of fundamental interactions. Intuitively, LCTs correspond to linear combinations of energy-momentum and spacetime compatible with the principle of covariance.

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“…Like in [26] we define Isodispersion Linear Canonical Transformations (ILCTs) as the LCTs fulfilling the relation…”

Section: -Transformations Laws Of Reduced Operators and Ilctsmentioning

confidence: 99%

“…Like in [26], we may define Isodispersion LCTs (ILCTs) as the LCTs which leaves invariant the quantity †…”

Section: -Phase Space Representation and Lcts Properties In Multidime...mentioning

confidence: 99%

Section: -Conclusionmentioning

confidence: 99%

See 1 more Smart Citation

Linear Canonical Transformations in relativistic quantum physics

Ranaivoson¹,

Andriambololona²,

Rakotoson

et al. 2021

Phys. Scr.

Self Cite

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show abstract

“…According to our works [14] and [15], LCTs can be linked with many interesting physical problems like the generalization of Fourier and Lorentz transformations in the framework of a relativistic quantum theory and the study of the properties of elementary fermions of the Standard Model. Following this way, we have, for instance, established in [15] a new approach to explain the charges (electric charge, hypercharge and colors) of the elementary fermions. It was shown that the electric charge can be written as the sum of four terms, the weak hypercharge of five terms and the weak isospin of two terms.…”

Section: -Conclusionmentioning

confidence: 99%

Study on a Spinorial Representation of Linear Canonical Transformation

Andriambololona¹,

Ranaivoson²,

Rakotoson³

2019

IJAMTP

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This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial representation of linear canonical transformations. This description is started with the presentation of a suitable parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operator space. Then the establishment of the spinorial representation is deduced using the well-known relation existing between special pseudo-orthogonal and spin groups. The cases of one dimension and general multidimensional theory are both studied.

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

Cited by 2 publications

References 2 publications

Linear Canonical Transformations in relativistic quantum physics

Linear Canonical Transformations in relativistic quantum physics

Study on a Spinorial Representation of Linear Canonical Transformation

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