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In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…

Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…

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…

The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…

The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…

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…

The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy conservation argument is not obvious, an…

A review of old inconsistencies of Classical Electrodynamics (CED) and of some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation and of the electron equation of motion, and problems…

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 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…

The usual action integral of classical electrodynamics is derived starting from Lanczos's electrodynamics -- a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell's equations interpreted…

Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in framework of Maxwellian theory, a novel convection displacement current is…

We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Li\'enard-Wiechert field terms. The equations are…

An obstacle to the development of direct action version of electromagnetism was that in the end it failed to fulfill its initial promise of avoiding the problem of infinite Coulomb self-energy in the Maxwell theory of the classical point…

Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…

We develop a thermodynamic framework that couples mass dynamics, described by the Newton- Gibbs-van der Waals formalism, with electromagnetic fields beyond the scope of classical Maxwell theory. Classical Newtonian mechanics does not…

Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…

Electromagnetic duality of Maxwell theory is a symmetry of equations but not of the action. The usual application of the `complexity=action' conjecture would thus loose this duality. It was recently proposed in arxiv:1901.00014 that the…

Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…

Some inadequacy in the traditional description of the phenomenon of electro-magnetic field radiation created by a point charge moving along a straight line with an acceleration is found and discussed in this paper in detail. The possibility…