Related papers: High Energy Dirac Solutions: Issues and Ramificati…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
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…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
We study the solution of the diffusion equation for Ultra-High Energy Cosmic Rays in the general case of an expanding universe, comparing it with the well known Syrovatsky solution obtained in the more restrictive case of a static universe.…
We consider a Dirac electron in the presence of an exponentially decaying magnetic field. We obtain exact energy eigenvalues with a zero-energy state and the corresponding eigenfunctions. We also calculate the probability density and…
An exact solution of Lorentz-Dirac equations where the energy conservation law is violated, is described herein for the case of two charges.
We review in this talk some aspects of the exciting field of hyperon polarization phenomena in high energy reactions, over the last twenty years or so. On the experimental side, a large amount of significant polarization data for hyperon…
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present…
The two-dimensional Dirac equation has been widely used in graphene physics, the surface of topological insulators, and especially quantum scarring. Although a numerical approach to tackling an arbitrary confining problem was proposed…
These lectures discuss the mysteries involving the production and extragalactic propagation of ultrahigh energy cosmic rays and suggested possible solutions.
By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac…
We study $(2+1)$ dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another…
We discuss a problem concerning the ultrahigh energy neutrino propagation through the Earth. We present calculation of the neutrino-nucleon cross section at high energies, based on the unifed evolution equation at small x. We also show the…
We present a brief introduction to the physics of Ultra High Energy Cosmic Rays (UHECRs), concentrating on the experimental results obtained so far and on what, from these results, can be inferred about the sources of UHECRs.
We extend the method from [Naito, Naito, and Hashimoto, Phys. Rev. Research 5, 033189 (2023)] to solve the Dirac equation not only for the ground state but also for low-lying excited states using a deep neural network and the unsupervised…
An outlook on physics at the high energy frontier of nucleus-nucleus collisions is presented, on the basis of the new results presented at Quark Matter 2011 by the LHC and RHIC experiments.
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the…