Related papers: Maxwell's Equations in Complex Variables
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the \emph{cognoscenti} of differential forms on manifolds; namely, that charge conservation…
For the system of Maxwell equations of electromagnetism in an $l$-periodic composite medium of overall size $L$ ($0<l<L<\infty$), in the low-frequency quasistatic approximation, we develop an electromagnetic version of strain-gradient…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
In the R-Minkowski space-time, which we recently defined from an appropriate deformed Poisson brackets that reproduce the Fock coordinate transformation, we derive an extended form for Maxwell's equations by using a generalized version of…
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
Maxwell equation in geometric algebra formalism with equally weighted basic solutions is subjected to continuously acting Clifford translation. The received states, operators acting on observables, are analyzed with different values of the…
A fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the…
This paper presents a thorough investigation into nonradiating sources of Maxwell's equations. Various characterizations are developed to clarify the properties of nonradiating sources, considering their varying degrees of regularity.…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…
We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term that is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular…
In this paper, operator gauge transformation, first introduced by Kobe, is applied to Maxwell's equations and continuity equation in QED. The gauge invariance is satisfied after quantization of electromagnetic fields. Inherent nonlinearity…
Using to a minimum extent special relativity input, and relying on the Lorentz-force expression for the force acting on a charged particle in motion under the influence of electric (E) and magnetic (B) fields, the Maxwell curl equations are…
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…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…