Related papers: Generalized Maxwell equations for exterior-algebra…
We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations…
The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
In this paper, the directional derivatives in accordance with the orthonormal frame {T, N, B} are defined in $M_{q}^{3}(c)$, and the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the…
The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
This survey revisits classical results in vector calculus and analysis by exploring a generalised perspective on the exterior derivative, interpreting it as a measure of "infinitesimal flux". This viewpoint leads to a higher-dimensional…
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence…
We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy statistics can emerge…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
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 unified field is a Maxwell-Lorentz field. Maxwell-Lorentz equations for potentials in standard four-dimensional form are satisfied exactly. This is achieved by involving new fundamental field sources, strict definition of which requires…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
In the framework of the field theory it is shown that a time (viewed as a scalar temporal field) is an internal property of the physical system, which defines its causal structure and evolution. A new concept of internal time allows to…
This paper develops a general method to construct Ehrenfest-like relations for Lagrangian field theories when an external, coordinate-dependent scalar potential is applied. To do so, we derive continuity equations in which the spatial and…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…