Related papers: Dirac equation with a magnetic field in 3D non-com…
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin…
Starting from the Dirac equation coupled to a classical radiation field a set of equations of motion for charged quasi-particles in the classical limit for slowly varying radiation and matter fields is derived. The radiation reaction term…
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
We study the current of chiral charge density in a Dirac semimetal with two Dirac points in momentum space, subjected to an externally applied time dependent electric field and in the presence of a magnetic field. Based on the kinetic…
I investigate the quantum dynamics of a spin-$1/2$ particle in a static, spherically symmetric Einstein-Gauss-Bonnet (EGB) black-hole spacetime within the Hamiltonian framework. Starting from the Dirac equation in curved spacetime,…
Stability of matter with Coulomb forces has been proved for non-relativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic fields. In both cases stability requires that the fine…
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…
In this paper we study the motion of a charged particle on a Riemannian surface under the influence of a positive magnetic field B. Using Moser's Twist Theorem and ideas from classical pertubation theory we find sufficient conditions to…
We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary…
We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The Dirac…
We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the…
The Schr\"odinger equation is solved for the wave function of an electron moving in a superposition of external constant and uniform electric and magnetic fields at an arbitrary angle between the field directions. The changing of the…
We perform a comparative study for the magnetization dynamics within linear response theory of one and two dimensional massive Dirac electrons, after switching on either a real (hermitian) or an imaginary (non-hermitian) magnetic field.…
We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We…
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we…
The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…