Search Results (9)

The description of the internal spaces of fermion and boson fields with “basis vectors”, which are the superpositions of odd and even products of the operators ${\gamma }^a$, with the index a running in internal and external space-time, suggests in $d=2(2n+1)$-dimensions in internal space, such as $d=(13+1)$, and $d=(3+1)$ in external space-time, a unified picture of all so far observed fermions and bosons. Quarks, leptons, antiquarks, and antileptons appear in families - each family contains fermions and antifermions. Bosons—gravitons, photons, weak bosons, gluons, and scalars, which carry the spatial index $\alpha$ (for tensors and vectors $\alpha =n=$$(0,1,2,3)$ and for scalars $\alpha \ge 5$)—appear in two orthogonal groups. All fields are assumed to have non-zero momenta and angular momenta only in the $d=(3+1)$, $SO(3,1)$, of ordinary space-time. In any $d=2(2n+1)$-dimensional space, the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of bosons. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates “basis vectors” and their properties in $d=(13+1)$ and $d=(5+1)$. The article presents new results and discusses open problems with this theory. Full article

We present a spectral-action framework for connecting generalized trace dynamics (GTD) to the structural form of the low-energy action of the observed Universe. The fundamental single-STM-atom Lagrangian is decomposed exactly into a purely bosonic sector, boson–fermion cross terms, and bifermionic terms. This sectorwise decomposition furnishes a dictionary to almost-commutative spectral geometry: the bosonic sector supplies a quadratic GTD Dirac functional built from the six split-biquaternionic differential directions together with octonionic vector/gauge fluctuations; the cross-sector supplies, under an explicit localization hypothesis, a sesquilinear fermionic pairing; and the bifermionic sector supplies the scalar/internal channel that is bosonized into the Higgs bridge field. We also record the principal-symbol link between the $\mathrm{SO}(3,3)$ BF variables and the four-dimensional leafwise Dirac operator. The two four-dimensional leaves of the six-dimensional base overlap in two common directions; from the observed (gravitational) leaf, the two nonintersecting directions of the complementary leaf are internal, so the second leaf is reinterpreted as the weak-interaction sector rather than as an independent spacetime—a reinterpretation stated here as an explicit hypothesis. Under stated assumptions—spontaneous localization, Euclidean continuation, six- to four-dimensional BF reduction, and a candidate observed-leaf finite geometry compatible with the $E_6/J_3\left({\mathbb{O}}_{\mathbb{C}}\right)$ inputs—the bosonic heat-kernel expansion yields the structural low-energy classes of terms: Einstein–Hilbert gravity, Yang–Mills kinetic terms, and scalar kinetic and potential terms. In addition, we provide a candidate finite spectral triple with explicit finite trace invariants, verify that the localization map respects the one-generation lepton/quark representation split, identify visible color-singlet scalar channels with electroweak quantum numbers $(\mathbf{1},\mathbf{2},\pm 1/2)$, and exhibit a smooth regulator family with explicit cutoff moments $(f_0,f_2,f_4)$. Conversely, the assembled low-energy spectral action admits a natural inverse bilinear lift back to split bioctonionic trace dynamics. Every arrow of the construction is classified as an exact algebraic identity, an imported result, a working hypothesis, or an open problem. Under this classification, the paper offers a possible architecture for obtaining low-energy gauge–gravity physics from GTD, with conditional consistency checks and reductions; it is not a completed first-principles derivation of the Standard Model coupled to gravity. Full article

One of the most important and unanswered problems in particle physics is the origin of the three generations of quarks and leptons. The Standard Model does not provide any hint regarding its sequential charge assignments, which remain a fundamental mystery of Nature. One possible solution of the puzzle is to look for charge assignments, in a given gauge theory, that are inter-generational, by employing the cancellation of the gravitational and gauge anomalies horizontally. The 331 model, based on an $SU{\left(3\right)}_C\times SU{\left(3\right)}_L\times U{\left(1\right)}_X$ does this in an economical way and defines a possible extension of the Standard Model, where the number of families has necessarily to be three. We review the model in Pisano, Pleitez, and Frampton’s formulation, which predicts the existence of bileptons. Another characteristics of the model is to unify the $SU{\left(3\right)}_C\times SU{\left(2\right)}_L\times U{\left(1\right)}_X$ into the 331 symmetry at a scale that is in the TeV range. Expressions of the scalar mass eigenstates and of the renormalization group equations of the model are also presented. Full article

The new stable fermion family, with Standard Model electroweak (EW) charges, should take part in sphaleron transitions in the early Universe before breaking of the EW symmetry. The conditions of balance between the excess of new fermions (additional generation of new superheavy U, D quarks and new E, N leptons) and baryon asymmetry, were considered at temperatures above, and below, the phase transition, using a system of equations for chemical potentials. Full article

In this paper, we study the effect of electroweak sphaleron transition and electroweak phase transition (EWPT) in balancing the baryon excess and the excess stable quarks of the 4th generation. Sphaleron transitions between baryons, leptons and the 4th family of leptons and quarks establish a definite relationship between the value and sign of the 4th family excess and baryon asymmetry. This relationship provides an excess of stable $\overline{U}$ antiquarks, forming dark atoms—the bound state of ($\overline{U}\overline{U}\overline{U}$) the anti-quark cluster and primordial helium nucleus. If EWPT is of the second order and the mass of U quark is about 3.5 TeV, then dark atoms can explain the observed dark matter density. In passing by, we show the small, yet negligible dilution in the pre-existing dark matter density, due to the sphaleron transition. Full article

The effect of the electroweak sphaleron transition in balance between baryon excess and and the excess of stable quarks of 4th generation is studied in this paper. Considering the non-violation of $SU\left(2\right)$ symmetry and the conservation of electroweak and new charges and quantum numbers of the new family, it makes possible sphaleron transitions between baryons, leptons and 4th family of leptons and quarks. In this paper, we have tried to established a possible definite relationship between the value and sign of the 4th family excess relative to baryon asymmetry. If U-type quarks are the lightest quarks of the 4th family and sphaleron transitions provide excessive $\overline{U}$ antiquarks, asymmetric dark matter in the form of dark atom bound state of ($\overline{U}\overline{U}\overline{U}$) with primordial He nuclei is balanced with baryon asymmetry. Full article

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) × U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark–Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter–antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout–Englert–Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model. Full article

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of ${\gamma }^a$ ’s. Arranged into irreducible representations of “eigenvectors” of the Cartan subalgebra of the Lorentz algebra $S^{ab}$ $(=\frac{i}{2}{\gamma }^a{\gamma }^b{|}_{a\ne b})$ these objects form $2^{\frac{d}{2}-1}$ families with $2^{\frac{d}{2}-1}$ family members each. Family members of each family offer the description of all the observed quarks and leptons and antiquarks and antileptons, appearing in families. Families are reachable by ${\tilde{S}}^{ab}$ $=\frac{1}{2}{\tilde{\gamma }}^a{\tilde{\gamma }}^b{|}_{a\ne b}$ . Creation operators, carrying the family member and family quantum numbers form the basis vectors. The action of the operators ${\gamma }^a$ ’s, $S^{ab}$ , ${\tilde{\gamma }}^a$ ’s and ${\tilde{S}}^{ab}$ , applying on the basis vectors, manifests as matrices. In this paper the basis vectors in $d=(3+1)$ Clifford space are discussed, chosen in a way that the matrix representations of ${\gamma }^a$ and of $S^{ab}$ coincide for each family quantum number, determined by ${\tilde{S}}^{ab}$ , with the Dirac matrices. The appearance of charges in Clifford space is discussed by embedding $d=(3+1)$ space into $d=(5+1)$ -dimensional space. The achievements and predictions of the spin-charge-family theory is also shortly presented. Full article

Two knots; just two rudimentary knots, the unknot and the trefoil. That’s all we need to build a model of the elementary particles of physics, one with fermions and bosons, hadrons and leptons, interactions weak and strong and the attributes of spin, isospin, mass, charge, CPT invariance and more. There are no quarks to provide fractional charge, no gluons to sequester them within nucleons and no “colors” to avoid violating Pauli’s principle. Nor do we require the importation of an enigmatic Higgs boson to confer mass upon the particles of our world. All the requisite attributes emerge simply (and relativistically invariant) as a result of particle conformation and occupation in and of spacetime itself, a spacetime endowed with the imprimature of general relativity. Also emerging are some novel tools for systemizing the particle taxonomy as governed by the gauge group SU(2) and the details of particle degeneracy as well as connections to Hopf algebra, Dirac theory, string theory, topological quantum field theory and dark matter. One exception: it is found necessary to invoke the munificent geometry of the icosahedron in order to provide, as per the group “flavor” SU(3), a scaffold upon which to organize the well-known three generations—no more, no less—of the particle family tree. Full article