Related papers: Note on the Dirac Field in Real Domain
On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann-Liouville fractional derivatives, and that it is possible to…
We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the…
Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation.…
The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained by the direct derivation by standard methods of quantum field theory from exact solutions of the Dirac equation in the…
A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.
The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each…
The theory of mean field electrodynamics, now celebrating its fiftieth birthday, has had a profound influence on our modelling of cosmical dynamos, greatly enhancing our understanding of how such dynamos may operate. Here I discuss some of…
We investigate some peculiar aspects of the so called Lee-Wick Electrodynamics focusing on physical effects produced by the presence of sources for the vector field. The interactions between stationary charges distributions along parallel…
Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as a model of electron. It is shown that such singularities…
For the first time the exact analytical expressions for the three-dimensional bound electron states in the Coulomb field of the chain consisting of positively charged ions, are obtained within the Dirac description, using the new spinor…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…
Electromagnetic properties of hadrons can be computed by lattice simulations of QCD in background fields. We demonstrate new techniques for the investigation of charged hadron properties in electric fields. Our current calculations employ…
We derive the advection of magnetic fields due to gradients in magnetic diffusivity, starting from the magnetic induction equation. We discuss physical examples, and compare our results to those in the literature. Our induction and…
The Dirac point with a double-cone structure for optical fields, an optical analogy Dirac fermions in graphene, can be realized in optically homogenous metamaterials. The condition for the realization of Dirac point in optical systems is…
There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann…
Clifford number representation for linear electrodynamics with dyon sources is considered. Source function for the appropriate system of the first order equations for electromagnetic field is obtained. The field of an arbitrary moving point…