相关论文: Sedenion algebra for three lepton/quark generation…
An algebraic representation of three generations of fermions with $SU(3)_C$ color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ is constructed. Recent constructions based on division algebras convincingly describe a…
We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry $SU(3)_c\times U(1)_{em}$ can be described using the algebra of complexified sedenions $\mathbb{C}\otimes\mathbb{S}$. A primitive idempotent is…
We present a unified model without the need for an ad hoc Standard Model hypothesis; we explain why there are three generations of charged and neutral leptons, why neutrinos have a vanishingly small mass, and why flavor-mixing emerges and…
The exceptional euclidean Jordan algebra of 3x3 hermitian octonionic matrices, appears to be tailor made for the internal space of the three generations of quarks and leptons. The maximal rank subgroup of its automorphism group F4 that…
The Standard Model has three generations of fermions and although it does not contain any explicit reason for this, the existence of additional generations is now very constrained by experiment. Present measurements are saturating…
We construct an explicit algebraic realisation of three fermion generations within a single Clifford algebra, transforming under the full Standard Model $SU(3)_C\times SU(2)_L\times U(1)_Y$ gauge group, in which an intrinsic $S_3$ family…
Building on previous work, we extend an algebraic realisation of three fermion generations within the complex Clifford algebra $\mathbb{C}\ell(8)$ by incorporating a $U(1)_{em}$ gauge symmetry. The algebra $\mathbb{C}\ell(8)$ corresponds to…
We propose a viable theory based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge group supplemented by the $S_4$ discrete group together with other various symmetries, whose spontaneous breaking gives rise to the current SM fermion mass…
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…
In usual extended technicolor (ETC) theories based on the group ${\rm{SU}(N_{ETC}})_{ETC}$, the quarks of charge 2/3 and -1/3 and the charged leptons of all generations arise from ETC fermion multiplets transforming according to the…
A detailed and general study of the fermionic structure of the 331 models with \beta arbitrary is carried out based on the criterion of cancellation of anomalies. We consider models with an arbitrary number of lepton and quark generations,…
The application of fermion-boson symmetry to the standard model leads to the following: first, there are three generations of scalar quarks and scalar leptons in addition to the known quarks and leptons, and, secondly, the divergences in…
We report the results of an extensive numerical study of the $Sp(4)$ lattice gauge theory with three (Dirac) flavors of fermion in the two-index antisymmetric representation. In the presence of (degenerate) fermion masses, the theory has an…
Despite the enormous achievements, the Standard model of Particle physics can not be consider as complete theory of fundamental interactions. Among other things, it can not describe the gravitational interaction and it depends on 19…
A considerable amount of the standard model's three-generation structure can be realised from just the $8\hspace{.3mm}\mathbb{C}$-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can…
Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group $SU(3)$ and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to…
A fermion-boson-type composite model for quarks and leptons is proposed. Elementary fields are only one kind of spin-1/2 and spin-0 preon. Both are in the global supersymmetric pair with the common electric charge of e/6 and belong to the…
We study the lowest dimensional typical and atypical representations of SU(5/3) superalgebra as a possible unified gauge theory having a natural SU(5) subalgebra with SU(3) extra structure, which will be used to accommodate three…
The author's idea of {\it algebraic compositeness} of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. i) For all fundamental particles of…
We point out a somewhat mysterious appearance of $SU_c(3)$ representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found in the Clifford algebra $\mathbb{C}l(6)$, arising…