Related papers: On the initial value formulation of classical elec…
We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number…
The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the…
Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The…
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the…
We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime…
The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
Motivated by the initial value problem in semiclassical gravity, we study the initial value problem of a system consisting of a quantum scalar field weakly interacting with a classical one. The quantum field obeys a Klein-Gordon equation…