Related papers: A New Formulation of Electrodynamics
Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows to write a ``Dirac'' equation for the photon containing all the known properties of it. In…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
In the first part of the present work, we focus on the theory of gravitoelectromagnetism (GEM), and we derive the full set of equations and constraints that the GEM scalar and vector potentials ought to satisfy. We discuss important aspects…
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 note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the…