Related papers: Hamilton form of Maxwell equations and its general…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived…
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…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
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…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante…
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom…
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including…
This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades $r$ and $r-1$ respectively in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the Maxwell…
Charges are everywhere because most atoms are charged. Chemical bonds are formed by electrons with their charge. Charges move and interact according to Maxwell's equations in space and in atoms where the equations of electrodynamics are…
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…
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…