Related papers: High Energy Dirac Solutions: Issues and Ramificati…
I discuss recent progress in understanding the high-energy evolution in QCD, which points towards a remarkable correspondence with the reaction-diffusion problem of statistical physics.
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
We discuss the basic features of the propagation of Ultra High Energy Cosmic Rays in astrophysical backgrounds, comparing two alternative computation schemes to compute the expected fluxes. We also discuss the issue of the transition among…
Under appropriate assumptions the energy of wave equations with damping and variable coefficients $c(x)u_{tt}-\hbox{div}(b(x)\nabla u)+a(x)u_t =h(x)$ has been shown to decay. Determining the rate of decay for the higher order energies…
In this paper we determine solutions for the L\'evy-Leblond operator or a parabolic Dirac operator in terms of hypergeometric functions and spherical harmonics. We subsequently generalise our approach to a wider class of Dirac operators…
We present a brief historical overview of the classical theory of a radiating point charge, described by the Lorentz-Dirac equation. A recent development is the discovery of tunnelling of a charge through a potential barrier, in a…
Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the…
Spectacular results of pulsar observations in X-ray and gamma-ray domains gave a new boost to theoretical models of pulsar magnetospheric activity. A challenging aspect of these efforts is that lightcurves and broadband energy spectra of…
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Just after the Dirac equation was established, a number of physicists tried to comment on and solve the spectral problem for the Dirac Hamiltonian with the Coulomb field of arbitrarily large charge $Z$, especially with $Z$ that is more than…
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the…
Covergent eigensolutions of the Dirac Equation for a relativistic electron in an external Coulomb potential are obtained using the Lanczos Algorithm. A tri-diagonal matrix representation of the Dirac Hamiltonian operator is constructed…
The paper proposes an algorithm for regularization of the self-energy expressions for a Dirac particle that meets the relativistic and gauge invariance requirements.
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to…
Some neutrino predictions at the highest energies for a number of production mechanisms are comparatively reviewed in the light of future projects for neutrino detection.
In this paper we study the conditions, under which the quaternionic Riccati equations have periodic solutions. The obtained result we compare with one recently obtained important one.
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
The status of present theoretical description of very high energy hadronic interactions is reviewed. The impact of new results of accelerator and cosmic ray experiments on hadronic interaction model constructions is discussed in detail.…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It…