Related papers: On the relation between the Maxwell system and the…
Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…
This paper investigates the \emph{massive} Maxwell-Dirac system under the Lorenz gauge condition in (4+1) dimensional Minkowski space. The focus is on establishing global existence and scattering results for small solutions on the weighted…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
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 slightly generalized classical Maxwell electrodynamics can describe the…
The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of…
In a previous work we have described the classical structure and analyzed the interaction of the classical Dirac particle with uniform and oscillating electric and magnetic fields. In the present paper we consider the interaction of the…
Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
The Maxwell vector potential and the Dirac spinor used to describe the classical theory of electrodynamics both have components which are considered to be ordinary smooth functions on space-time. We reformulate electrodynamics by adding an…
The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the…
The Maxwell-Dirac equations are the equations for electronic matter, the "classical" theory underlying QED. In this article we examine the stationary Maxwell-Dirac equations under weak regularity and decay assumptions. We prove that: There…
Maxwell matter waves emerge from a perspective, complementary to de Broglie's, that matter is fundamentally a wave phenomenon whose particle aspects are revealed by quantum mechanics. Their quantum mechanical description is derived through…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical…
Recent experiments have demonstrated an interesting reaction on a gas-surface defined as epicatalysis. The non-equilibrium thermodynamic potentials were well described in a series of experiments. However the theoretical basis was not…
We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
Based on Maxwellian quaternionic electromagnetic theory, the octonionic hyper-strong field, hyper-weak field and the quantum interplays can be presented by analogy with octonionic electromagnetic, gravitational, strong and weak…
The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero…