Related papers: Ballistic dynamics of Dirac particles in electro-m…
We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which…
Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the…
The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of…
In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $\Delta$, there are two distinct Dirac points…
A 1D Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schr?odinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
In this paper we prove boundedness of propagators for Dirac equations with unbounded time-dependent potentials on Wiener amalgam spaces. In particular we deal with class of potentials such as including Stark and harmonic potentials.
The planar quantum dynamics of spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations are obtained directly from the planar Dirac equation with nonminimum coupling. New…
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector…
Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realm. As a result, a new dynamical constant for the electromagnetic field is identified and linked to the…
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Dirac's formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities…