Related papers: Nonlinear Maxwell equations
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space,…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
The interaction between charged particles through quasi-static fields must occur instantaneously; otherwise a violation of the energy principle would occur. As a consequence, the instantaneous transmission of both energy and information…
Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum).…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
The system of Maxwell equations with an initial condition in a vacuum is solved in a cylindrical coordinate system. It derives the cylindrical transverse electromagnetic wave mode in which the electric field and magnetic field are not in…
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different…
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…
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…
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…
In this work, a non-relativistic theory of the electroscalar field being an expansion of the classical Maxwell's electrodynamics is presented. Expansion of the classical electrodynamics is based on the hypothesis about an existing new…
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'…
We consider Maxwell fields associated with any shear-free null geodesic congruence on Minkowski or Riemannian background space-time. Bounded singular loci of these fields are treated as particle-like formations, possess "self-quantized"…
We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell's equations that preserves this symmetry. This new set of equations…