Related papers: Geometry of the Standard Model
We survey known results on the canonical bundle formula and its applications in algebraic geometry.
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
The purpose is to study systems of interacting particles in the Generl Relativity context, by the principle of least action using purely classical concepts. The particles are described by a state tensor using a Clifford algebra for the…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
I discuss the basic elements of the process that will lead to the discovery of possible new phenomena at the LHC. We review the status of the tools available to model the Standard Model backgrounds, and the role that such tools can play in…
We identify and study a matrix algebra consisting of Pascal-type matrices. The generator of the matrix algebra is shown to well define a canonical bundle map, called the Pascal map on jet bundles, and we use it to give an intrinsic…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
After a prologue which clarifies some issues left open in my last paper, the main features of the tetron model of elementary particles are discussed in the light of recent developments, in particular the formation of strong and electroweak…
In this article the current understanding of fundamental particles and their interactions is presented for the interested non-specialist, by adopting a semi-historical path. A discussion on the unresolved problems is also presented.
We present an introduction into the basic concepts of the Standard Model, i.e. the gauge theories of the forces and the Higgs mechanism for generating masses. The Glashow-Salam-Weinberg theory of the electroweak interactions will be…
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…
This is a historical account from my personal perspective of the development over the last few decades of the standard model of particle physics. The model is based on gauge theories, of which the first was quantum electrodynamics,…
After two decades of a development of the unitary and analytic models of the electromagnetic structure of hadrons and nuclei their main principles are briefly formulated, then a general scheme of their applications to the electromagnetic,…