We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to the initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and H−1 compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new...

In this note, we propose an exegesis of the Maxwell equations for electromagnetism. We begin with an analogy between the homogeneous Maxwell equations and the equations needed to describe the vorticity field of an incompressible inviscid fluid. We suggest that the inhomogeneous equations are analogous to two equations valid in turbulent hydrodynamics. Once the analogy is completed we give the m...

Dvoeglazov’s paper is not trivial because we know the classical definition of any non-trivial truth: a truth is not trivial if and only if an opposite statement is not false (and vice versa, of course). So I strongly recommend his paper for a reader. But I have a few notes: 1) V. Dvoeglazov writes in his footnote number 7: ”In my opinion, equations (20,21) of ref. [1] are just another form of t...

Maxwell equations are the basis of the theory of electromagnetic fields. In the stationary case they split into independent problems for electric and magnetic fields. For the electric field in conductive media electrical conductivity problem is formulated, and in insulators the problem of electrostatics is formulated. Equations for stationary problems are of elliptic type, whereas in general th...

The Maxwell-Dirac equations are the equations for electronic matter, the “classical” theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell-Dirac system has ψ = eφ, with φ independent of t. The system is said to be isolated if the independent variables obey quite weak regularity and decay conditions. In this p...

Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss’s laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to der...

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 particular passive, isolated circuit could present a growth of its currents. Resolution of this problem is sought within the context of the usual electromag...

We present solution generating methods which allow us to construct exact static solutions to the equations of four-dimensional Einstein-MaxwellDilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling...

We study the symmetries of the two dimensional Heterotic string theory by following the approach of Kinnersley et al for the study of stationary axially-symmetric Einstein-Maxwell equations. We identify the finite dimensional symmetries which are the analogues of the groups G and H ′ for the Einstein-Maxwell equations. We also give the constructions for the infinite number of conserved currents...