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Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
Following an approach proposed by Rosser for deriving the transformation equations of volume charge density and current density we derive the transformation equations for the space-time coordinates of the same event, for the mass and the…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
We set up a vacuum theory of gravity with an extra dimension of vanishing proper length. The most general solution to the field equations are presented. This formulation is free of Kaluza-Klein modes and does not allow the propagation of…
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional…
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
The construction of conformally invariant gauge conditions for Maxwell and Einstein theories on a manifold M is found to involve two basic ingredients. First, covariant derivatives of a linear gauge (e.g. Lorenz or de Donder), completely…
A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent in local symmetry. The…
We generalize duality invariance for the free Maxwell action in an arbitrary background geometry to include the presence of electric and magnetic charges. In particular, it follows that the actions of equally charged electric and magnetic…
A simple derivation is given of the Einstein-Maxwell field equations from the 2nd ordinary exterior differential of a precursor to the soldering form for n-dimensional differentiable manifolds having a general linear connection and in…
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…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
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…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their…
Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass,…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…