Related papers: The Helmholtz Theorem and Superluminal Signals
In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method…
We look afresh at the deduction of the "Lorentz contraction" of a "rod" from the Lorentz transformation equations of the special theory of relativity. We show that under special conditions, which include acceleration of the "rod", length…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
In this paper, we further develop a recently proposed theory of time based on wavefunction collapse in general relativity. It is based on the postulations that quantum states, which violate the momentum and Hamiltonian constraints,…
A uniqueness theorem for time-harmonic electromagnetic fields which requires the normal components of electromagnetic fields specified on a spherical surface is proposed and proved. The statement of the theorem is : "For a spherical volume…
With the help of the Seiberg-Witten map, one can obtain an effective action of a deformed QED from a noncommutative QED. Starting from the deformed QED, we investigate the propagation of photons in the background of electromagnetic field,…
The transformation converting equations invariant under Lorentz into the equations invariant under Galileo is obtained. On this basis: (1) the super-light electromagnetic wave with longitudinal and transversal modes is found out; (2) it is…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
The vector potential is a fundamental concept widely applied across various fields. This paper presents an existence theorem of a vector potential for divergence-free functions in $W^{m,p}(\mathbb{R}^N,\mathbb{T})$ with general $m,p,N$.…
We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by…
The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the…
Developing on the ideas of R. Stora and coworkers, a formulation of two dimensional field theory endowed with extended conformal symmetry is given, which is based on deformation theory of holomorphic and Hermitian spaces. The geometric…
Assume that in a Lorentzian frame is given a relativistically admissible trajectory of a point mass. An event in such a frame can be described by four coordinates, first three representing the position and the last one the time of the…
This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century,…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number…
We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild-de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is…