Related papers: On the initial value formulation of classical elec…
In this paper we use the classical electrodynamics to show that the Lorenz gauge can be incompatible with some particular solutions of the d Alembert equations for electromagnetic potentials. In its turn, the d Alembert equations for the…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell…
The demonstration that the electromagnetic fields derived from the Lienard-Wiechert potentials do not satisfy the Maxwell equations is proved to be false. Errors were made in the computation of the derivatives of retarded quantities. The…
The self-force problem of classical electrodynamics has two closely linked facets: The ill defined dynamics of a point charge due to the divergent self field at the position of the charge, and the divergence of formally conserved…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
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…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…
The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory Maxwell's homogeneous equations correspond to a…
In this letter we study the self-energy of a point-like charge for the electromagnetic field in a non minimal Lorentz symmetry breaking scenario in a $n+1$ dimensional space time. We consider two variations of a model where the Lorentz…
Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists.…
Retarded electromagnetic potentials are derived from Maxwell's equations and the Lorenz condition. The difference found between these potentials and the conventional Li\'{e}nard-Wiechert ones is explained by neglect, for the latter, of 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…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…
In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function whose spatial and temporal derivatives transform the instantaneous…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
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…
Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference…
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has…
We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell…