Related papers: The Unified Standard Model
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest…
This thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra. Here, we argue that physical concepts such as particles, causality, and irreversible time may result from the…
We interpret the elements of the exceptional Lie algebra $\mathfrak{e}_{8(-24)}$ as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra…
Building upon previous works, it is shown that two minimal left ideals of the complex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of $\mathbb{C}\ell(4)$ transform as one generation of leptons and quarks under the gauge…
The paper surveys recent progress in the search for an appropriate internal space algebra for the Standard Model (SM) of particle physics. As a starting point serve Clifford algebras involving operators of left multiplication by octonions.…
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…
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold…
There are many ways to embed the Lie groups of the Standard Model of Particle Physics in a Lie group of type $E_8$, but so far there is no convincing demonstration that the finite symmetries (and asymmetries) of weak hypercharge, three…
The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent…
The Standard Model of the theory of elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three…
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
We model physical signals using elements of the algebra of split octonions over the field of real numbers. Elementary particles are corresponded to the special elements of the algebra that nullify octonionic norms (zero divisors). It is…
The Standard Model of particle physics is built on the principle of local gauge symmetry. This work provides a pedagogical introduction for advanced undergraduates by using quantum electrodynamics (QED) as the simplest example of a gauge…
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
We propose an $E_8 \otimes E_8$ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space. Each of the $E_8$ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion…
The observed Standard Model is consistent with the existence of vector-like species with electric charge a multiple of $e/6$. The discovery of a fractionally charged particle would provide nonperturbative information about Standard Model…
We determine all Lie groups compatible with the gauge structure of the Standard Elementary Particle Model (SM) and their representations. The groups are specified by congruence equations of quantum numbers. By comparison with the…
The Standard Model of elementary particles is a theory unifying three of the four basic forces of the Nature: electromagnetic, weak, and strong interactions. In this paper we consider the Standard Model in the presence of a classical…
The Standard Model of particle physics is derived from first principles from the free Dirac Lagrangian in 8-dimensional spacetime. Motivated by second quantization arguments, we embed the 4-dimensional Clifford algebra of the Dirac…
In accordance with known phenomenological facts on leptons and quarks in the Standard Model as well as on the scale of neutrino masses and introducing the supersymmetry, we logically substantiate the unique composition of fundamental…