Related papers: Note on the Dirac Field in Real Domain
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are…
Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in…
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled electromagnetic field and Maxwell field with Dirac current as source. Our particular interest is the static case in which the Dirac current is purely time-like --…
In this work, the action of the relativistic electron is derived from the hydrodynamic formulation of the Dirac equation. In particular, in the hydrodynamic scenario, the four-velocity of the electron is regarded as an Eulerian field and…
A brief review of the different ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet are formulated. In our approach the Dirac equation is derived from the…
In this paper we obtain exact solutions of a 2D relativistic Dirac oscillator in the presence of a constant magnetic field. We compute the energy spectrum and discuss its dependence on the spin and magnetic field strength.
The particle creation by the so-called peak electric field is considered. The latter field is a combination of two exponential parts, one exponentially increasing and another exponentially decreasing. We find exact solutions of the Dirac…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual…
Quantization of free Dirac fields is formulated in terms of a reducible representation of CAR. Similarly to the bosonic case we arrive at field operators which are indeed operators and not operator valued distributions. Observables such as…
We study the problem of the quantization of the massive charged Dirac field on a naked Reissner-Nordstr\"{o}m background. We show that the introduction of an anomalous magnetic moment for the electron field allows a well--defined quantum…
We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…
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…
We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space. We solve this problem…
The paper is concerned with the basis properties of root function systems of the Dirac operator with a complex-valued summable potential. We establish a necessary condition of convergence of corresponding spectral expansions.
In the paper a new class of exact localized solutions of Dirac's equation in the field of a circularly polarized electromagnetic wave and a constant magnetic field is presented. These solutions possess unusual properties and are applicable…
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…