Related papers: Relativistic electron wave packets carrying angula…
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…
We study the oscillations and conversions of relativistic neutrinos propagating in matter of variable density using the wave packet formalism. We show how the oscillation and coherence lengths are modified in comparison with the case of…
Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum…
The classical and quantum representations of thermal equilibrium are strikingly different, even for free, non-interacting particles. While the first involves particles with well-defined positions and momenta, the second usually involves…
In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincar\'e group. We define a weaker…
Stationary electromagnetic waves display aspects that are shared with massive particles, since the energy and momentum contained in a volume of sides equal to the wavelengths form a non-zero energy-momentum invariant. The parallel can be…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
We have studied the phase singularity of the relativistic vortex beams for the two sets of relativistic operators. One includes the new spin and orbital angular momentum (OAM) operators, which is derived from the parity-extended Poincar\'e…
The transverse properties of an electron beam are characterized by two quantities, the emittance which indicates the electron beam extend in the phase space and the angular momentum which allows for non-planar electron trajectories. Whereas…
The annular electron beam has significant practical potential in high-energy physics and condensed matter physics, which can be used to edge-enhancement electron imaging, collimation of antiprotons in conventional linear accelerators,…
The effective interaction between two classical nonrelativistic electrons (positrons) in the presence of intense electromagnetic radiation (one and two waves) is theoretically studied. Small relativistic corrections are taking into account…
A theoretical description of vortex electrons interacting with electric and magnetic fields is presented, based on Lorentz transformations. The general dynamical equations of motion of a twisted electron with intrinsic orbital angular…
The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar…
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an objective extra space dimension. "Particle"…
A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained…
Correct and complete (to terms of $\vec{v} / c$ -- $\vec{v}$ is particle's velocity, $c$ is the speed of light) derivation of equation of motion for real dust particle under the action of electromagnetic radiation is derived. The effect of…
Equation of motion of an uncharged arbitrarily shaped dust particle under the effects of (stellar) electromagnetic radiation and thermal emission is derived. The resulting relativistically covariant equation of motion is expressed in terms…
The interaction between freely propagating electrons and light waves is typically described using an approximation in which we assume that the electron velocity remains approximately the same during the interaction. In this article we…