Related papers: 3D transformation for point rotating reference fra…

The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…

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 idea of determining the magnetic resonance condition in a rotating frame of reference is being studied. In this frame, the rotating magnetic field should be at rest. The 3D transformation that determines the transition to the frame 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…

We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a…

We study the evolution of neutrinos electroweakly interacting with a rotating matter. The description of neutrinos is based on the Dirac equation in the corotating noninertial frame where matter is at rest. We find solution of this Dirac…

We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…

Although the standard generally-covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the…

We consider the transformation for the point rotation frames with the angle, spatial coordinate along the axis of rotation and time as variables. The problem arises when light, propagating through 3-fold electrooptical crystal, is modulated…

Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the…

Parameters of localization are defined in the lab and rotating frame for solutions of the Dirac equation in the field of a traveling circularly polarized electromagnetic wave and constant magnetic field. The radius of localization is of the…

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 concept of a rotating reference frame with the axis of rotation at each point and the applicability of this concept to different areas of physics. The transformation for the transition from the resting to rotating frame is…

The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non…

The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…

We consider the problem of internal particle state transformation, which is a bound state of several constituents, from the particle's rest frame to the system in which this particle is relativistic. It is assumed that in the rest frame of…

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…

In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from rewriting the Dirac equation in a form adapted to a…

We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted…