Related papers: On the Pre-metric Formulation and Nonlinearization…
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…
It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
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…
Force-free electrodynamics is the theoretical paradigm used to describe electromagnetic fields in a region where the inertia of plasma is negligible compared to the strength of the electromagnetic field. While these fields are studied…
We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux…
Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. \textbf{39}, 10909 (2006); Czech. J. Phys. \textbf{56}, 1269 (2006)) presented a $D+1$-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which…
This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature.…
This paper describes the electrodynamics of a null and force-free field in completely geometric terms. As was previously established in \cite{Menon_FF20}, solutions to force-free electrodynamics are governed by the existence of certain…
We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's…
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…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to…
The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed…
A framework for premetric p-form electrodynamics is proposed. Independently of particular constitutive relations, the corresponding Maxwell equations are derived as a special case of stress theory in geometric continuum mechanics.…
The notion of observers' and their measurements is closely tied to the Lorentzian metric geometry of spacetime, which in turn has its roots in the symmetries of Maxwell's theory of electrodynamics. Modifying either the one, the other, or…
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background does exist. This is nonlinearity essentially different from…
The main focus of this work is to study magnetic soft charges of the four dimensional Maxwell theory. Imposing appropriate asymptotic falloff conditions, we compute the electric and magnetic soft charges and their algebra both at spatial…