Related papers: On a Connection between the Maxwell System, the Ex…

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…

The Minkowski's theory is regarded as the classical approach for describing the electromagnetism of uniformly moving objects by elegantly utilizing the format-invariance of the Maxwell's equations in inertia reference frames under Lorentz…

We quantize a generalized electromagnetism in 2 + 1 dimensions which contains a higher-order derivative term by using Dirac's method. By introducing auxiliary fields we transform the original theory in a lower-order derivative one which can…

Using the weak field approximation, we can express the theory of general relativity in a Maxwell-type structure comparable to electromagnetism. We find that every electromagnetic field is coupled to a gravitoelectric and gravitomagnetic…

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…

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We…

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…

We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…

Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…

We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems which describe large particle ensembles interacting by either electromagnetic fields or a relativistic scalar gravity model. For both systems we derive a radiation…

The Maxwell integral equations expressing Ampere's and Faraday's laws are shown to be affected by heavy physical approximations. The usual deduction from them, moreover, of the corresponding set of differential Maxwell equations is based,…

The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…

The issue of justifying the eddy current approximation of Maxwell's equations is re-considered in the time-dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits.

In this paper we consider some new classical effects obtained for a planar electrodynamics with the presence of a higher order derivatives term. The model can be interpreted as a kind of extension for the $3d$ Maxwell-Chern-Simons…

We consider the Wheeler-De Witt equation as a device for finding eigenvalues of a Sturm-Liouville problem. In particular, we will focus our attention on the electric (magnetic) Maxwell charge. In this context, we interpret the Maxwell…

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by…

We take the Gauss' linking integral of two curves as a starting point to discuss the connection between the equation of continuity and the inhomogeneous Maxwell equations. Gauss' formula has been discussed before, as being derivable from…

We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…

Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the…