Related papers: Mathematical Paradoxes of Dirac Equation Represent…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
We discuss some aspects of the gravitational interaction of the relativistic quantum particles with spin 1/2. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. The…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\"{o}dinger--Pauli theory. We here…
We consider the most general axial torsion completion of gravity with electrodynamics for $\frac{1}{2}$-spin spinors in an $8$-dimensional representation of the Dirac matter field: this theory will allow to define antimatter as matter with…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot…
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties…
Electrons in low-temperature solids are governed by the non-relativistic Schr$\ddot{o}$dinger equation, since the electron velocities are much slower than the speed of light. Remarkably, the low-energy quasi-particles given by electrons in…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is…
Errors pertaining to the following physical theories are discussed: the Dirac magnetic monopole theory; the Klein-Gordon equation; the Yukawa theory of nuclear force; the idea of Vector Meson Dominance; the Aharonov-Bohm effects; the idea…
The magnetic force is retained in the Lorentz Oscillator Model and a perturbation solution is derived beyond the dipole approximation. Perturbation series for the electric dipole, magnetic dipole, and electric quadrupole moments in addition…
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…
The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are…
In recent times there has been a renewed interest in the force experienced by a charged-particle with anomalous magnetic moment in the presence of external fields. In this paper we address the basic question of the force experienced by a…
The quantum fluctuations of the Dirac field in external classical gravitational and electromagnetic fields are studied. A self-consistent equation for torsion is calculated, which is obtained using one-loop fermion diagrams.