Related papers: On the evolutionary form of the constraints in ele…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the…
On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations…
The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante…
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…
We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa,…
We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
Pleba\'nski's class of nonlinear vacuum electrodynamics is considered which is for several reasons of interest at the present time. In particular the question is answered under which circumstances Maxwell's original field equations are…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…
This paper describes recent progress in the analysis of relativistic gauge conditions for Euclidean Maxwell theory in the presence of boundaries. The corresponding quantum amplitudes are studied by using Faddeev-Popov formalism and…
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of…
The goal of this work was to investigate the propagation of the constraints in the ghost-free bimetric theory where the evolution equations are in standard 3+1 form. It is established that the constraints evolve according to a first-order…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe…