arXiv subjects

Norma Susana Mankoc Borstnik

Publications and source records attributed to Norma Susana Mankoc Borstnik.

At least 19 recordsLinked to original sources

arXiv2025

Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included? Relation with strings theories

The article proposes the description of internal spaces of fermion (quarks and leptons and antiquarks and antileptons) and boson (photons, weak bosons, gluons, gravitons and scalars) second quantized fields in a unique way if they all are massless. The internal spaces are described by ``basis vectors'', which are the superposition of odd (for fermions) and even (for bosons) products of the operators $γ^ {a}$. For an arbitrary symmetry $SO(d-1,1)$ of the internal spaces, it is the number of fermion fields (they appear in families and have their Hermitian conjugated partners in a separate group) equal to the number of boson fields (they appear in two orthogonal groups), manifesting a kind of supersymmetry, which differ of the string supersymmetry. On the assumption that fermions and bosons are active (they have momenta different from zero) only in $d=(3+1)$ ordinary space-time, bosons present vectors if they carry the space index $μ=(0,1,2,3)$, and present scalars if they carry the index $σ\ge 5$. The author discusses this theory's latest achievements, with a trial to understand whether the extension to strings or to odd-dimensional spaces can lead to a new kind of supersymmetry. This model, named {\it spin-charge-family} theory, manifests in a long series of papers on the phenomenological success of the theory in elementary particle physics and cosmology.

physics.gen-ph↗

arXiv2025

A trial to understand the supersymmetry relations through extension of the second quantized fermion and boson fields, either to strings or to odd dimensional spaces

The article studies the extension of the internal spaces of fermion and boson second quantized fields, described by the superposition of odd (for fermions) and even (for bosons) products of the operators $γ^ {a}$, to strings and odd dimensional spaces.\\ For any symmetry $SO(d-1,1)$ of the internal spaces, it is the number of fermion fields (they appear in families and have their Hermitian conjugated partners in a separate group) equal to the number of boson fields (they appear in two orthogonal groups), manifesting a kind of supersymmetry, which differs from the usual supersymmetry.\\ The article searches for the supersymmetry arising from extending the ``basis vectors'' of second quantized fermion and boson fields described in $d=2(2n+1)$ (in particular $d=(13+1)$) either to strings or to odd-dimensional spaces ($d=2(2n+1)+1$).

physics.gen-ph↗

arXiv2023

How Clifford algebra helps understand second quantized quarks and leptons and corresponding vector and scalar boson fields, {\it opening a new step beyond the standard model}

This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators $γ^a$. While the Clifford odd "basis vectors" manifest properties of fermion fields, appearing in families, the Clifford even "basis vectors" demonstrate properties of the corresponding gauge fields. In $d\ge (13+1)$ the corresponding creation operators manifest in $d=(3+1)$ the properties of all the observed quarks and leptons, with the families included, and of their gauge boson fields, with the scalar fields included, making several predictions. The properties of the creation and annihilation operators for fermion and boson fields are illustrated on the case $d=(5+1)$, when $SO(5,1)$ demonstrates the symmetry of $SU(3)\times U(1)$.

hep-th↗

arXiv2022

How Clifford algebra can help understand second quantization of fermion and boson fields

In the review article in Progress in Particle and Nuclear Physics (vol.121(2021) 103890)) the authors present the achievements so far of the spin-charge-family theory, which offers the explanation for all the so far observed properties of elementary fermion and boson fields, if the space-time is higher than d=(3+1), it must be $d\ge (13+1)$. Fermions interact with gravity only. Ref. PPNP (vol.121(2021) 103890)) presents, in addition to a rather detailed review of all the achievements of this theory so far, also an explanation for the postulates of the second quantization for fermionic fields: The internal space of fermions described with "basis vectors" represented by the Clifford odd objects manifests all the properties of fermion fields, including the anticommutativity of their creation and annihilation operators. This paper shows that even Clifford algebra objects provide a description of the internal space of boson fields manifesting all known properties of boson fields, explaining as well the reasons for the second quantization postulates for boson fields. Properties of fermion and boson fields with the internal spaces described by the Clifford odd and Clifford even objects are demonstrated on the toy model with $d=(5+1)$.

physics.gen-ph↗

arXiv2022

Proceedings to the 24rd International Workshop "What Comes Beyond the Standard Models", July 5 -- July 11, 2021, Bled, Slovenia, [Virtual Workshop -- July 5.--11. 2021]

Contributions of the participants of the 24th International Workshop "What Comes Beyond the Standard Models", July 5 to July 11, 2021, Bled, Slovenia, presented either with the arxiv number of each contribution or with the webside of the Proceedings published by DMFA, ZALOlZNISTVO LJUBLJANA, DECEMBER 2021.

physics.gen-ph↗

arXiv2021

How do Clifford algebras show the way to the second quantized fermions with unified spins, charges and families, and to the corresponding second quantized vector and scalar gauge fields

This contribution presents properties of the second quantized not only fermion fields but also boson fields, if the second quantization of both kinds of fields origins in the description of the internal space of fields with the ''basis vectors'' which are the superposition of odd (when describing fermions) or even (when describing bosons) products of the Clifford algebra operators $γ^a$'s. The tensor products of the ''basis vectors'' with the basis in ordinary space forming the creation operators manifest the anticommutativty (of fermions) or commutativity (of bosons) of the ''basis vectors'', explaining the second quantization postulates of both kinds of fields. Creation operators of boson fields have all the properties of the gauge fields of the corresponding fermion fields, offering a new understanding of the fermion and boson fields.

physics.gen-ph↗

arXiv2021

How does Clifford algebra show the way to the second quantized fermions with unified spins, charges and families, and with vector and scalar gauge fields beyond the {\it standard model}

Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are many proposals in the literature for the next step. The spin-charge-family theory of one of us (N.S.M.B.) is offering the explanation for not only all by the standard model assumed properties of quarks and leptons and antiquarks and antileptons, with the families included, of the vectors gauge fields, of the Higgs's scalar and Yukawa couplings, but also for the second quantization postulates of Dirac and for cosmological observations, like there are the appearance of the dark matter, of matter-antimatter asymmetry, making several predictions. This theory proposes a simple starting action in $ d\ge (13+1)$ space with fermions interacting with the gravity only, what manifests in $d=(3+1)$ as the vector and scalar gauge fields, and uses the odd Clifford algebra objects to describe the internal space of fermions, what enables that the creation and annihilation operators for fermions fulfill the anticommutation relations for the second quantized fields without Dirac's postulates: Fermions single particle states already anticommute. We present in this review article a short overview of the spin-charge-family theory, illustrating shortly on the toy model the breaks of the starting symmetries in $d=(13+1)$ space, which are triggered either by scalar fields -- the vielbeins with the space index belonging to $d>(3+1)$ -- or by the condensate of the two right handed neutrinos, with the family quantum number not belonging to the observed families. We compare properties and predictions of this theory with the properties and predictions of $SO(10)$ unifying theories.

physics.gen-ph↗

arXiv2018

Fermions and bosons in the expanding universe by the spin-charge-family theory

The spin-charge-family theory, which is a kind of the Kaluza-Klein theories in $d=(13+1)$ --- but with the two kinds of the spin connection fields, the gauge fields of the two Clifford algebra objects, $S^{ab}$ and $\tilde{S}^{ab}$ --- explains all the assumptions of the standard model: The origin of the charges of fermions appearing in one family, the origin and properties of the vector gauge fields of these charges, the origin and properties of the families of fermions, the origin of the scalar fields observed as the Higgs's scalar and the Yukawa couplings. The theory explains several other phenomena like: The origin of the dark matter, of the matter-antimatter asymmetry, the "miraculous" triangle anomaly cancellation in the standard model and others. Since the theory starts at $d=(13+1)$ the question arises how and at which $d$ had our universe started and how it came down to $d=(13+1)$ and further to $d=(3+1)$. In this short contribution some answers to these questions are presented.

physics.gen-ph↗

arXiv2017

The Spin-Charge-Family theory offers the explanation for all the assumptions of the Standard model, for the Dark matter, for the Matter-antimatter asymmetry, making several predictions

The spin-charge-family theory, which is a kind of the Kaluza-Klein theories but with fermions carrying two kinds of spins (no charges), offers the explanation for all the assumptions of the standard model, with the origin of families, the higgs and the Yukawa couplings included. It offers the explanation also for other phenomena, like the origin of the dark matter and of the matter/antimatter asymmetry in the universe. It predicts the existence of the fourth family to the observed three, as well as several scalar fields with the weak and the hyper charge of the standard model higgs ($\pm \frac{1}{2}, \mp \frac{1}{2}$, respectively), which determine the mass matrices of family members, offering an explanation, why the fourth family with the masses above $1$ TeV contributes weakly to the gluon-fusion production of the observed higgs and to its decay into two photons, and predicting that the two photons events, observed at the LHC at $\approx 750$ GeV, might be an indication for the existence of one of several scalars predicted by this theory.

hep-ph↗

arXiv2017

Spin-charge-family theory is offering next step in understanding elementary particles and fields and correspondingly universe

More than 40 years ago the standard model made a successful new step in understanding properties of fermion and boson fields. Now the next step is needed, which would explain what the standard model and the cosmological models just assume: a. The origin of quantum numbers of massless one family members. b. The origin of families. c. The origin of the vector gauge fields. d. The origin of the Higgses and Yukawa couplings. e. The origin of the dark matter. f. The origin of the matter-antimatter asymmetry. g. The origin of the dark energy. h. And several other open problems. The spin-charge-family theory, a kind of the Kaluza-Klein theories in $(d=(2n-1) +1)$ - space-time, with $d=(13+1)$ and the two kinds of the spin connection fields, which are the gauge fields of the two kinds of the Clifford algebra objects anti-commuting with one another, may provide this much needed next step. The talk presents: i. A short presentation of this theory. ii. The review over the achievements of this theory so far, with some not published yet achievements included. iii. Predictions for future experiments.

hep-ph↗

arXiv2017

Are superheavy stable quark clusters viable candidates for the dark matter?

The explanation for the origin of families of quarks and leptons and their properties is one of the most promising ways to understand the assumptions of the Standard Model. The Spin-Charge-Family theory, which does propose the mechanism for the appearance of families and offers an explanation for all the assumptions of the Standard Model, predicts two decoupled groups of four families. The lightest of the upper four families has stable members, which are correspondingly candidates to constitute the dark matter. We study the weak and the "nuclear" (determined by the colour interaction among the heavy fifth family quarks) scattering of such a very heavy baryon by ordinary nucleons in order to show that the cross-section is very small and consistent with the observation in most experiments so far, provided that the quark mass of this baryon is about 100 TeV or above.

hep-ph↗

arXiv2015

Can the spin-charge-family theory explain baryon number non conservation?

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.

hep-ph↗

arXiv2013

Can we predict the fourth family masses for quarks and leptons?

In the spin-charge-family theory four massless families of quarks and leptons before the electroweak break are predicted. Mass matrices of all the family members demonstrate in this proposal the same symmetry, determined by the family groups. There are scalar fields - two $SU(2)$ triplets, the gauge fields of the family quantum numbers, and three singlets, the gauge fields of the three charges ( $Q, Q'$ and $Y'$)- all doublets with respect to the weak charge, which determine mass matrices on the tree level and, together with other contributions, also beyond the tree level. The symmetry of mass matrices remains unchanged for all loop corrections. The three singlets are, in loop corrections also together with other contributors, responsible for the differences in properties of the family members. Taking into account by the spin-charge-family theory proposed symmetry of mass matrices for all the family members and simplifying study by assuming that mass matrices are Hermitian and real and mixing matrices real, we fit free parameters of mass matrices to experimental data within the experimental accuracy. Calculations are in progress.

hep-ph↗

arXiv2013

Properties of twice four families of quarks and leptons, of scalars and gauge fields as predicted by the spin-charge-family theory

The spin-charge-family theory, proposed by the author as a possible new way to explain the assumptions of the standard model, predicts at the low energy regime two decoupled groups of four families of quarks and leptons. In two successive breaks the massless families, first the group of four and at the second break the rest four families, gain nonzero mass matrices. The families are identical with respect to the charges and spin. There are two kinds of fields in this theory, which manifest at low energies as the gauge vector and scalar fields: the fields which couple to the charges and spin, and the fields which couple to the family quantum numbers. In loop corrections to the tree level mass matrices both kinds start to contribute coherently. The fourth family of the lower group of four families is predicted to be possibly observed at the LHC and the stable of the higher four families -- the fifth family -- is the candidate to constitute the dark matter. Properties of the families of quarks and leptons and of the scalar and gauge fields, before and after each of the two successive breaks, bringing masses to fermions and to boson fields are analysed and relations among coherent contributions of the loop corrections to fermion properties discussed, including the one which enables the existence of the Majorana neutrinos. The relation of the scalar fields and mass matrices following from the {\em spin-charge-family} theory to the {\it standard model} Yukawa couplings and Higgs is discussed. Although effectively the scalar fields manifest as Higgs and Yukawas, measurements of the scalar fields do not coincide with the measurement of the Higgs.

hep-ph↗

arXiv2013

How can the Standard model Higgs and also the extensions of the Higgs to Yukawa's scalars be interpreted in the spin-charge-family theory and to what predictions about the Higgs does this theory lead?

This contribution is to show how does the spin-charge-family theory interpret the assumptions of the standard model, and those extensions of this model, which are trying to see the Yukawa couplings as scalar fields with the family (flavour) charges in the fundamental representations of the group. The purpose of these contribution is i.) to try to understand why the standard model works so well, although its assumptions look quite artificial, and ii.) how do predictions of the spin-charge-family theory about the measurements of the scalar fields differ from predictions of the {\em standard model}, which has only one scalar field - the Higgs - and also from its more or less direct extensions with Yukawas as the scalar dynamical fields with the family charge in the fundamental or anti-fundamental representation of group.

hep-ph↗

arXiv2013

Do we have the explanation for the Higgs and Yukawa couplings of the standard model?

The spin-charge-family theory offers a possible explanation for the assumptions of the standard model, interpreting the standard model as its low energy effective manifestation. The theory predicts several scalar fields determining masses and mixing matrices of fermions and weak bosons. The scalar fields manifest as doublets with respect to the weak charge, while they are triplets with respect to the family quantum numbers. Since free scalar fields (mass eigen states) differ from those which couple to $Z_m$ and to $W^{\pm}_{m}$ or to each family member of each of the family the spin-charge-family theory predictions for LHC might differ from those of the standard model.

hep-ph↗

arXiv2012

How many scalar fields there are and how are they related to fermions and weak bosons in the spin-charge-family theory?

The spin-charge-family theory offers a possible explanation for the assumptions of the standard model, interpreting the standard model as its low energy effective manifestation. The standard model Higgs and Yukawa couplings are explained as an effective replacement for several scalar fields, all of bosonic (adjoint) representations with respect to all the charge groups, with the family groups included. Assuming the Lagrange function for all scalar fields to be of the renormalizable kind, properties of the scalar fields on the tree level are discussed. Free scalar fields (mass eigenstates) differ from either those, which couple to $Z_m$, or to $W^{\pm}_{m}$ or to each family member of each of the four families, which further differ among themselves. Consequently the spin-charge-family theory predictions differ from those of the standard model.

hep-ph↗

arXiv2011

The spin-charge-family theory is explaining the origin of families, of the Higgs and the Yukawa couplings

The spin-charge-family theory offers a possible explanation for the assumptions of the standard model - for the charges of a family members, for the gauge fields, for the appearance of families, for the the scalar fields - interpreting the standard model as its low energy effective manifestation. The spin-charge-family theory predicts at the low energy regime two decoupled groups of four families of quarks and leptons. The predicted fourth family waits to be observed, while the stable fifth family is the candidate to form the dark matter. The Higss and Yukawa couplings are the low energy effective manifestation of several scalar fields, all with the bosonic (adjoint) representations with respect to all the charge groups, with the family groups included. Properties of the families are analysed and relations among coherent contributions of the loop corrections to fermion properties discussed, including the one which enables the existence of the Majorana neutrinos. The appearance of several scalar fields is presented, their properties discussed, it is explained how these scalar fields can effectively be interpreted as the {\em standard model} Higgs (with the fermion kind of charges) and the Yukawa couplings, and a possible explanation why the Higgs has not yet been observed offered. The relation to proposals that the Yukawas follow from the SU(3) family (flavour) group, having the family charges in the fundamental representations of these groups, is discussed. The spin-charge-family theory predicts that there are no supersymmetric partners of the observed fermions and bosons.

physics.gen-ph↗