Related papers: Knots and the Maxwell Equations
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell…
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015a) (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the…
In this paper the Maxwell field theory is considered on the $Z_n$ symmetric algebraic curves. As a first result, a large family of nondegenerate metrics is derived for general curves. This allows to treat many differential equations arising…
In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the…
Source-free so-called ModMax theories of nonlinear electrodynamics in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations -- and as a function of a single real and positive parameter -- of…
Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's…
Pleba\'nski's class of nonlinear vacuum electrodynamics is considered which is for several reasons of interest at the present time. In particular the question is answered under which circumstances Maxwell's original field equations are…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We set up a correspondence between solutions of the Yang-Mills equations on ${\mathbb R}\times S^3$ and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we…
A reduction of the Dirac-Maxwell equations in the case of static cylindrical symmetry is performed. The behaviour of the resulting system of o.d.e.'s is examined analytically and numerical solutions presented. There are two classes of…
We draw connections between contact topology and Maxwell fields in vacuo on 3-dimensional closed Riemannian submanifolds in 4-dimensional Lorentzian manifolds. This is accomplished by showing that contact topological methods can be applied…
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
We introduce and examine a collection of unusual electromagnetic disturbances. Each of these is an exact, monochromatic solution of Maxwell's equations in free space with looped electric and magnetic field lines of finite extent and a…
In this paper the Maxwell field theory is considered on a closed and orientable Riemann surface of genus $h>1$. The solutions of the Maxwell equations corresponding to nontrivial values of the first Chern class are explicitly constructed…