Related papers: Electromagnetism and geometry
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
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 combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
The discovery of Electromagnetism by Oersted (1820) started an 'extraordinary decennium' ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several experiments, the electromagnetic induction was…
Our understanding of the four basic concepts of Physics -- space, time, matter and force -- has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to…
As documented by textbooks, the teaching of electromagnetic induction in university and high school courses is primarily based on what Feynman labeled as the ``flux rule'', downgrading it from the status of physical law. However, Maxwell…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
Issuing from a geometry with nonmetricity and torsion we build up a classical theory of gravitation and electromagnetism. The theory is coordinate covariant as well Weyl-gauge covariant. Massless and massive photons, intrinsic electr. and…
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…
Gauge theory, which is the basis of all particle physics, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. In this short lecture course I shall try to give an introduction to…