Related papers: On the relation between the Maxwell system and the…
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms…
We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein-Gordon equation. A simple linear interaction and a nonlinear perurbation produce solutions of the equations containing hylomorphic…
In this paper we study in detail the connection between the solutions to the Dirac and Weyl equation and the associated electromagnetic 4-potentials. First, it is proven that all solutions to the Weyl equations are degenerate, in the sense…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…
The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and…
Invoking Maxwell's classical electrodynamics in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of linear and angular momentum exchange…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
In a previous study it was demonstrated that Dirac's relativistic quantum equation for free electrons (DRQM)can be obtained from Maxwell's classical electromagnetic field equations (MaxEq). This raises fundamental issues about the…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum…
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…
Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down…
We show that the Maxwell equations for arbitrary inhomogeneous media are equivalent to a single quaternionic equation which can be considered as a generalization of the Vekua equation for generalized analytic functions.
Elements of a new model of strong interactions are described. The model is based on an extension of electrodynamics that is derived from a regular Lagrangian density. Here the electric and magnetic fields of Maxwell equations play a…
The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…
In this lecture we discuss some interesting developments in the modern theory of electromagnetic field(s). In particular, by using the methods developed in Dirac's constraint dynamics we derive the Schr\"{o}dinger equation for the free…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged…