Sterile neutrinos existence suggested from LCT covariance

Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Rakotoson, Hanitriarivo; Raboanary, R.

doi:10.1088/2399-6528/ac2409

Cited by 1 publication

(11 citation statements)

References 17 publications

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“…The eigenvalue equation (9) can be itself deduced from the relation (12) and the commutation relation in (11). We have also the well-known relations ð13Þ which justify the name ladder operators for and .…”

mentioning

confidence: 67%

“…Some operators related to LCTs and their representations were already considered by various authors [5][6][7]. However, the quadratic operators that are identified in this work are new ones even if some of them can be considered as generalization of operators introduced in the references [10][11][12].…”

Section: Introductionmentioning

confidence: 80%

“…Linear Canonical Transformations (LCTs) can be considered as generalization of some useful integral transformations like Fourier and Fractional Fourier Transforms. They are studied and used in many areas [1][2][3][4][5][6][7][8][9][10][11][12]. In quantum theory, they can be identified as the linear transformations which keep invariant the Canonical Commutation Relations (CCRs) defining the coordinates and momenta operators.…”

Section: Introductionmentioning

confidence: 99%

“…In quantum theory, they can be identified as the linear transformations which keep invariant the Canonical Commutation Relations (CCRs) defining the coordinates and momenta operators. In the references [11,12], it was shown that a covariance principle related with LCTs may play an important role in physics and in the establishment of a unified theory of fundamental interactions. In the present work, our main objective is to identify some quadratic operators that are invariant under the action of LCTs and to highlight their potential importance in physics.…”

Section: Introductionmentioning

confidence: 99%

“…The unitary transformation (14) is also known as a Bogolioubov transformation. The LCT-invariance of the Hamiltonian can also be seen through the relations (12) and (14).…”

mentioning

confidence: 99%

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Invariant quadratic operators associated with linear canonical transformations and their eigenstates

Ranaivoson¹,

Andriambololona²,

Rakotoson³

et al. 2022

J. Phys. Commun.

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The main purpose of this work is to identify invariant quadratic operators associated with Linear Canonical Transformations (LCTs) which could play important roles in physics. In quantum physics, LCTs are the linear transformations which keep invariant the Canonical Commutation Relations (CCRs). In this work, LCTs corresponding to a general pseudo-Euclidian space are considered and related to a phase space representation of quantum theory. Explicit calculations are firstly performed for the monodimensional case to identify the corresponding LCT-invariant quadratic operators then multidimensional generalizations of the obtained results are deduced. The eigenstates of these operators are also identified. A first kind of LCT-invariant operator is a second order polynomial of the coordinates and momenta operators. The coefficients of this polynomial depend on the mean values and the statistical variances-covariances of the coordinates and momenta operators themselves. It is shown that these statistical variances-covariances can be related with thermodynamic variables. In this context, new quantum corrections to the ideal gas state equation are deduced from correction to the Hamiltonian operator of non-relativistic free quantum particles that is suggested by LCT-covariance. Two other LCT-invariant quadratic operators, which can be considered as the number operators of some quasiparticles, are also identified: the first one is a number operator of bosonic type quasiparticles and the second one corresponds to fermionic type. This fermionic LCT-invariant quadratic operator is directly related to a spin representation of LCTs. It is shown explicitly, in the case of a relativistic pentadimensional theory, that the eigenstates of this operator can be considered as basic quantum states of elementary fermions. A classification of the fundamental fermions, compatible with the Standard Model of particle physics, is established from a classification of these states.

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mentioning

confidence: 67%

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The unitary transformation (14) is also known as a Bogolioubov transformation. The LCT-invariance of the Hamiltonian can also be seen through the relations (12) and (14).…”

mentioning

confidence: 99%

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