In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that weakly generalized classical Maxwell electrodynamics can describe the intraatomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic s...

Computational electromagnetism is concerned with the numerical study of Maxwell equations. By choosing a discrete Gaussian measure on prism lattice, we use discrete exterior calculus and lattice gauge theory to construct discrete Maxwell equations in vacuum case. We implement this scheme on Java development plateform to simulate the behavior of electromagnetic waves.

Using a technique based on dimensional descent, we show that Wigner's little group for massless particles, which acts as a generator of gauge transformation for usual Maxwell theory, has an identical role even for topologically massive gauge theories. The examples of B ∧ F theory and Maxwell-Chern-Simons theory are analyzed in details.

A new formalism of beam-optics and polarization has been recently presented, based on an exact matrix representation of the Maxwell equations. This is described in Part-I and Part-II. In this Part, we present the application of the above formalism to the specific example of the axially symmetric graded index fiber. This formalism leads to the wavelength-dependent modifications of the six aberra...

After reviewing the context in which Euclidean propagation is useful we compare and contrast Euclidean and Lorentzian Maxwell-Einstein theory and give some examples of Euclidean solutions.

In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE ) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21ψ̃, wh...

Fractional curl operator has been used to derive solutions to the Maxwell equations for fractional rectangular cavity resonator. These solutions to the Maxwell equations may be regarded as fractional dual solutions. Behavior of field lines and surface current density in fractional cavity resonator have been investigated with respect to the fractional parameter. Fractional parameter describes th...

An example of application of the specialized computer algebra system GRGEC to the searching for solutions to the source-free Maxwell and Einstein–Maxwell equations is demonstrated. The solution involving five arbitrary functions of two variables is presented in explicit form (up to quadratures).