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We inquire into classical and quantum laws of motion for the point charge sources in the nonlinear Maxwell-Born-Infeld field equations of classical electromagnetism in flat and curved Einstein spacetimes.
It is conventionally believed that solutions of so called "free" Maxwell equations for \varrho=0 (density of charge) describe the free electromagnetic field in empty space (if one considers the free field as a field, whose flux lines…
A survey on the dynamical and thermodynamical properties of plasmas with strong Coulomb interactions in the quasi-classical density-temperature region is given. First the basic theoretical concepts describing nonideality are discussed. 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…
We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell system that possess arbitrarily large charge densities and electric fields. In particular, we construct spherically symmetric solutions that describe a thin shell…
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…
In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically…
A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…
In the direct action form of classical EM we give the equation of motion for a classical massless bare charge without self-interaction in the presence of an external field. That equation permits superluminal speeds and time-reversals, and…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
The exact Li$\acute{e}$nard-Wiechert solutions for the point charge in arbitrary motion are shown to be null fields everywhere. These are used as a basis to introduce extended electromagnetic field equations that have null field solutions…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…
The solutions of the reduced Maxwell-Bloch equations for an anisotropic two-level medium, which describe the propagation of electromagnetic pulses having a duration from a few field oscillations, are studied. An influence of the permanent…
We study scalar massless and electromagnetic fields from static sources in a static higher dimensional spacetime. Exact expressions for static Green's functions for such problems are obtained in the background of the Majumdar-Papapetrou…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the…