Related papers: An Algebraic Roadmap of Particle Theories, Part II…
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric…
In these lectures I shall explain how a new-found nonabelian duality can be used to solve some outstanding questions in particle physics. The first lecture introduces the concept of electromagnetic duality and goes on to present its…
The Standard Model (SM) of particle physics is in such good agreement with experiment that it is still accepted as providing an accurate model of reality. Nevertheless, its algebraic foundations are in need of repair. Chirality is shown to…
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 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…
Peering in from the outside, $\mathbb{A} := \mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$ looks to be an ideal mathematical structure for particle physics. It is 32 $\mathbb{C}$-dimensional: exactly the size of one full…
The reader surely knows what particles physics is about: finding building blocks of nature that appear elementary at a given time and study their interactions - so why in the world this essay? The problem is how to arrive at a fundamental…
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…
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…
We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R-symmetry larger than R-parity, provided that the supersymmetric Standard Model can be minimally embedded into a grand unified…
In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$…
These four lectures constitute a gentle introduction to what may lie beyond the standard model of quarks and leptons interacting through $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ gauge bosons, prepared for an audience of graduate students in…
The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of…
Symmetries in the Physical Laws of Nature lead to observable effects. Beyond regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well defined breaking, as the…
The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the…
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…
Simply based on CP arguments, we argue against a Standard Model explanation of the baryon asymmetry of the universe in the presence of a first order phase transition. A CP-asymmetry is found in the reflection coefficients of quarks hitting…
Although there have been many experimental and theoretical efforts to measure and interpret small deviations from the standard model of particle physics, the gap that the model leaves in understanding why there are only three generations of…
In this manuscript, we show that three fundamental building blocks are supporting the Cosmological Principle. The first of them states that there is a special frame in the universe where the spatial geometry is intrinsically homogeneous and…
We stress the importance of the circa 20 parameters in the Standard Model, which are not fixed by the model but only determined experimentally, as a window to the physics beyond the Standard Model. However, it is a tiny window in as far as…