Related papers: Mathematical Paradoxes of Dirac Equation Represent…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…
The relativistic semiclassical evolution of the position of an electron in the presence of an external electromagnetic field is studied in terms of a Newton equation that incorporates spin effects directly. This equation emerges from the…
We investigate the possibility of coexistence between Dirac-like monopoles and Lorentz-violating electrodynamics. For this purpose, we study three distinct models: Myers-Pospelov, Ellis et al. and Gambini-Pullin. In particular, we find that…
The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask…
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…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
This paper examines the theory of electron magnetic dipole moment interactions with magnetic fields or other electrons in classical and quantum electrodynamics. We show that these interactions may be described by a version of the Poynting…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation…
The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze…
By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
The canonical quantization of $D=2n$ dimensional Dirac spinning particle in the external electromagnetic field is carried out in the gauge which allows to describe simultaneously particles and antiparticles (massive and massless) already at…
By analogy with the octonionic electromagnetic and gravitational interactions, the octonionic strong and weak interactions and their quantum interplays are discussed in the paper. In the weak interaction, the study deduces some conclusions…
Dirac and Weyl semimetals, materials where electrons behave as relativistic fermions, react to position- and time-dependent perturbations, such as strain, as if emergent electromagnetic fields were applied. Since they differ from external…
In this contribution we study the Dirac equation for a finite size proton in an external electric field with explicit introduction of Dirac-Pauli form factors. Our aim is twofold. On the one hand, we wish to study whether our conclusions…
We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…