A microscopic approach to quark and lepton masses and mixings

Lampe, Bodo

doi:10.1142/s0217751x15500256

Cited by 5 publications

(12 citation statements)

References 109 publications

(441 reference statements)

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“…How does this work out in detail? Mathematically, a tetron is assumed to transform as the fundamental spinor representation of SO (6,1). This representation is 8-dimensional and sometimes called the octonion representation.…”

Section: Small Neutrino Masses From Conservation Of Isospinmentioning

confidence: 99%

“…In reality, the Hamiltonian is somewhat more complicated than (5) due to the appearance of antitetrons and of the fact that inner-and inter-tetrahedral interactions are present, the inner ones with 'exchange coupling' j = −O(1) GeV (strong interaction scale) and the inter ones with J = O(100) GeV (weak interaction scale). j and J have different sign, because j leads to the frustrated 'antiferromagnetic' ground state of a single tetrahedron, while J is responsible for the 'ferromagnetic' 4 alignment of neighboring tetrahedrons [1].…”

Section: Small Neutrino Masses From Conservation Of Isospinmentioning

confidence: 99%

“…In this talk some important implications of the tetron model [1,2,3,4] of particle physics and cosmology will be reviewed. The universe is an elastic medium composed of invisible constituents which are bound at Planck energy.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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From Neutrino Masses to the Full Size of the Universe

Lampe¹

2021

Preprint

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Our universe is an elastic substrate of invisible tiny constituents, called tetrons, bound with bond length about the Planck length and binding energy the Planck energy. Tetrons transform as the fundamental fermion(=octonion) representation of SO(6,1). With respect to physical 3+1 spacetime a tetron is simply an isospin doublet of Dirac spinors Ψ = (U, D). The 24 known quarks and leptons arise as eigenmode excitations of a tetrahedral fiber structure, which is made up from 4 tetrons and extends into 3 additional 'internal' dimensions. While the laws of gravity are due to the elastic properties of the tetron bonds, particle physics interactions take place within the internal fibers. I will concentrate on two of the most intriguing features of the model:-understanding small neutrino masses from the conservation of isospin, and, more in general, calculating the spectrum of quark and lepton masses. This is obtained from the tetron model's interpretation of the Higgs mechanism.-the possibility to determine the full size of the universe from future dark energy measurements. This is obtained from the tetron model's interpretation of the dark energy phenomenon.Finally, the dark energy equation of state, i.e. the equation of state of the tetron background will be derived.

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Section: Small Neutrino Masses From Conservation Of Isospinmentioning

confidence: 99%

Section: Small Neutrino Masses From Conservation Of Isospinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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From Neutrino Masses to the Full Size of the Universe

Lampe¹

2021

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“…The crystal symmetry of superconductors does not allow us to consider the point groups of higher symmetry, such as the icosahedral group and its 4D extensions. However, this can be extended by considering the symmetry groups in the internal isospin space 25,26 .…”

Section: B Dirac Superconductorsmentioning

confidence: 99%

Dirac and Weyl fermions: from Gor’kov equations to Standard Model (in memory of Lev Petrovich Gor’kov), "Письма в Журнал экспериментальной и теоретической физики"

Volovik

2017

Письма в Журнал экспериментальной и теоретической физики

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Gor'kov theory of superconductivity 1 opened the application of the methods of quantum field theory to condensed matter physics. Later the results became relevant to relativistic quantum fields.PACS numbers: I. INTRODUCTIONApplication of quantum field theory to condensed matter physics began in Soviet Union around 1956-57 2 . In this approach the Fermi sea serves as an analog of the relativistic quantum vacuum -the Dirac sea. The Gor'kov theory of superconductivity 1 has been the fundamental step in this direction, which in turn triggered the development of the relativisic theories. The composite models developed by Nambu and Jona-Lasinio 3 and by Vaks and Larkin 4 , where the Higgs bosons appear as a composite states of the fermion pairs, are the direct consequences of the Gor'kov theory. In such models the original Weyl fermions of Standard Model (such as top quarks) play the role of the electrons in metals, while the composite Higgs bosons are analogs of the collective modes of the order parameter in superconductors. Here we consider another consequence of the Gor'kov theory of superconductivity, where the Weyl fermions emerge in superconductors as Bogoliubov quasiparticles. This in particular takes place for superconductors of the symmetry class O(D 2 ), where the 4 left-handed and 4 right-handed topologically protected chiral fermions emerge 5,6 , see Fig. I. Expansion of the Gor'kov Green's function in the vicinity of each topologically protected Weyl point leads to the effective relativistic quantum field theory with effective gauge fields and the effective gravity. This provides the hint for possible emergent origin of the "fundamental" Weyl fermions, gauge fields, and general relativity 8-10 .

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On the Relations between Fermion Masses and Isospin Couplings in the Microscopic Model

Lampe

2024

Fortschritte der Physik

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Quark and lepton masses and mixings are considered in the framework of the microscopic model. The most general ansatz for the interactions among tetrons leads to a Hamiltonian involving Dzyaloshinskii‐Moriya (DM), Heisenberg and torsional isospin forces. Diagonalization of the Hamiltonian provides for 24 eigenvalues which are identified as the quark and lepton masses. While the masses of the third and second family arise from DM and Heisenberg type of isospin interactions, light family masses are related to torsional interactions among tetrons. Neutrino masses turn out to be special in that they are given in terms of tiny isospin non‐conserving DM, Heisenberg and torsional couplings. The approach not only leads to masses, but also allows to calculate the quark and lepton eigenstates, an issue, which is important for the determination of the CKM and PMNS mixing matrices. Compact expressions for the eigenfunctions of are given. The almost exact isospin conservation of the system dictates the form of the lepton states and makes them independent of all the couplings in . As a consequence, a parameter‐free analytic expression for the PMNS matrix is derived which fits numerically all the measured matrix components. The formula includes a prediction of the leptonic Jarlskog invariant . An outlook is given on the treatment of the CKM matrix.

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A microscopic approach to quark and lepton masses and mixings

Cited by 5 publications

References 109 publications

From Neutrino Masses to the Full Size of the Universe

From Neutrino Masses to the Full Size of the Universe

Dirac and Weyl fermions: from Gor’kov equations to Standard Model (in memory of Lev Petrovich Gor’kov), "Письма в Журнал экспериментальной и теоретической физики"

On the Relations between Fermion Masses and Isospin Couplings in the Microscopic Model

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