Related papers: Electromagnetism and geometry
Contents. 1. Introduction. 2. Kinematics of a Material Medium: Material Representation. 3. Kinematics of a Material Medium: Convected Differentials. 4. Kinematics of a Perfect Elastic Medium. 5. Small Gravitational Perturbations of an…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
The Faraday-Ampere laws of electro-magnetic induction are formulated in terms of plain and twisted differential forms, taking in due account the body motion in terms of Lie time-derivatives. Covariance of Lie derivatives with respect to…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…
Two-dimensional pure electrodynamics is mapped into two-dimensional gravity in the first order formalism at classical and quantum levels. Due to the fact that the degrees of freedom of these two theories do not match, we are enforced to…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in…
This paper presents an alternative prerelativistic approach to the vacuum case of classical electrodynamics represented by vacuum Maxwell equations. Our view is based on the understanding that the corresponding differential equations should…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
This is a paper about geometry and how one can derive several fundamental laws of physics from a simple postulate of geometrical nature. The method uses monogenic functions analysed in the algebra of 5-dimensional spacetime, exploring the…
A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from QED, has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory…
Using non-excessively-technical language and written in informal style, this article introduces the reader to the concepts of electromagnetic and gravitational waves and recounts the prediction of existence of these waves by Maxwell and…
In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
The quantum field theory in the presence of classical background electromagnetic fields is reviewed. We give a pedagogical introduction to the Feynman-Furry method of describing non-perturbative interactions with very strong electromagnetic…