Related papers: Space-time orientations and Maxwell's equations
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
Space-time-modulated systems have attracted significant interest over the past decade due to their ability to manipulate electromagnetic waves in unprecedented ways. Here, we introduce a new type of space-time-modulated structure, the…
Extended guiding-center Vlasov-Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-time-scale orderings. The guiding-center…
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory,…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic…
A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
This paper examines the Maxwell system of electrodynamics within the framework of distributions. A primary objective is to establish boundary conditions for fields at interfaces when the charge and current densities are measures localized…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not…
In this article we will explore the spacetime phase structure inside the Infeld-van der Waerden formalisms, showing that Maxwell's theory in this scenario leads to an axion-like phase electrodynamics, which suggests that this phase may…
Generalizing of the Maxwell field to nonlinear electrodynamics theories, we look for the magnetic solutions. In initial approximation these models give the usual linear electrodynamics. We consider a suitable metric and investigate the…
We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell…
A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…
The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…