Related papers: Generally Covariant Maxwell Theory for Media with …
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
It is pointed out that the previous energy-momentum tensors of Minkowski and Abraham for the electromagnetic field in continuous media are based on a covariant formulation which does not reflect a symmetry inherent to the system. Instead,…
This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress-energy-momentum tensors in the classical description of continuous polarizable perfectly insulating media. While…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
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…
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…
The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the…
Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
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,…
In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…
Maxwell's equations and the Lorentz force density are expressed using an alternative simultaneity gauge. As a result, they describe electrodynamics for an observer travelling with a constant velocity through an isotropic medium. If desired,…
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 examines the Maxwell system of electrodynamics within the framework of distributions. A primary objective is to establish boundary conditions for fields at interfaces when the charge and current densities are measures localized…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like…
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…