Related papers: The Dirac algebra and grand unification
The present work provides a new conceptual framework for GUT (Grand Unified Theory) based on a picture of fractal universe. Under a hypothesis of multi-scaled matter structure, we find new clues for the conciliation of quantum and…
We present a unification model based on the well-known but mysterious cubic-structure grouping of quarks and leptons that suggests an underlying symmetry connection deemed explainable by a unified theory. It results in an extension of the…
In a previous work it was shown that the gravitational and inertial masses are correlated by an adimensional factor, which depends on the incident radiation upon the particle. It was also shown that there is a direct correlation between the…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
The Standard Model of particle physics was established based on the equivalence principle and gauge invariance. The Lagrangians were built upon experimental data demonstrating the violation of discrete symmetries together with ideas of…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
We present formulae for the calculation of Dirac gaugino masses at leading order in the supersymmetry breaking scale using the methods of analytic continuation in superspace and demonstrate a link with kinetic mixing, even for non-abelian…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar…
The Dirac equation may be thought as originating from a theory of five-dimensional (5D) space-time. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time…
We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…
Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black…
We consider the possibility that Dirac neutrino masses may be a manifestation of chiral symmetry breaking via non-perturbative QCD dynamics. The key role played by light quarks in this mechanism can naturally lead to signals that are…
Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special ``neutrino'' symmetries. If not…
The Dirac theory implies the existence of an internal vector space, in addition to spin space. Using Dirac's coupling of variables in internal space to those in physical space, we construct a new configuration structure for particles in the…
This paper discovers geometric unification theory of the grand unification and gravitational interactions and their new physics according to the general fiber bundle theory, symmetry and so on. Consequently, the research of this paper is…
This paper contains applications of the quantum theory for gravity developed in the paper " A Sketch for a Quantum Theory of Gravity". Firstly, it is shown that the theory gives a direct derivation of the implications of Dirac's large…
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption…
On basis of an algebraic analysis of symmetry breaking in general and the Higgs mechanism in the standard model of elementary particles we generalize the concept of symmetry breaking to systems with non-compact groups but not necessarily…