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Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field…
In the present paper a geometrization of electrodynamics is proposed which makes use of a generalization of Riemannian geometry considered already by Einstein and Cartan in the 20ies. Cartan's differential forms description of a…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive…
A supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. This formulation generalizes the known action for scalar charged particles investigated…
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for…
Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with…
We investigate a theory of time-symmetric action-at-a-distance electrodynamic or gravitational interactions where the four-forces depend only on the electric charges, the rest masses, the position four-vectors, and the four-velocities of…
We consider the electromagnetic field occurring in the background of a static, axially symmetric vacuum solution of Einstein's field equations immersed in an external magnetic field. The solution, known as the $\gamma$ metric (or…
A geometrical approach to calculate the electric field due to a uniformly charged rod is presented. The result is surprisingly simple and elegant. Using pure geometrical quantities like length and angle, the direction of the electric field…
The eigenspinor approach uses the classical amplitude of the algebraic Lorentz rotation connecting the lab and rest frames to study the relativistic motion of particles. It suggests a simple covariant extension of the common definition of…
A mathematically interesting hyperbolic solution to the Einstein field equations is studied on an eight-dimensional pseudo-Riemannian manifold $\mathbb{X}_{4,4}$ that is a spacetime of four space dimensions and four time dimensions. [The…
New electrodynamics with quaternionic mass is found to yields interesting results. The quaternionic mass involves longitudinal as well as transverse (vector) masses. Because of these two masses, an application of a magnetic field in a…
This paper revisits the geometric foundations of electromagnetic theory, by studying Faraday's concept of field lines. We introduce "covariant electromagnetic field lines," a novel construct that extends traditional field line concepts to a…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet…
We present a formulation of Quantum Electrodynamics in terms of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge…
We pursue a coherent analysis of hyperbolically symmetric static sources by extending the work of Herrera \cite{26} to the case of electromagnetic field. We deeply analyze the impact of such a force on the physical characteristics of the…
We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…