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A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in…
The intention of this course is to provide guidance and tools necessary to carry out an analytical design of a simple accelerator magnet. Basic concepts and magnet types will be explained as well as important aspects which should be…
This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…
Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first…
The following notes are intended to provide a brief primer in plasma physics, introducing common definitions, basic properties and processes typically found in plasmas. These concepts are inherent in contemporary plasma-based accelerator…
The foundations of matrix geometry are discussed, which provides the basis for recent progress on the effective geometry and gravity in Yang-Mills matrix models. Basic examples lead to a notion of embedded noncommutative spaces (branes)…
We look at the foundations of electromagnetism in this 1st LeCosPA Symposium. For doing this, after some review (constraints on photon mass etc.), we use two approaches. The first one is to formulate a Parametrized Post-Maxwellian (PPM)…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
In the previous papers (quant-ph/0204037), (quant-ph/0204134) on the basis of Dirac's equation we have considered the electromagnetic interpretation of the quantum theory of electron. Here we continue the electron structure study. Since the…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometry.
The full non-linear structure of the action and transformation rules for $\W_N$-gravity coupled to matter are obtained from a non-linear truncation of those for $w_ \infty$ gravity. The geometry of the construction is discussed, and it is…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…