Related papers: Spurious Modes in Dirac Calculations and How to Av…

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…

We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…

In this article, we investigate the relativistic quantum dynamics of spin-$\frac{1}{2}$ particles in (1+2)-dimensional G\"{u}rses space-time backgrounds, and analyze the effects on the eigenvalues. We solve the Dirac equation using the…

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a…

The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…

Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

It has been observed that a quantum mechanical theory need not to be Hermitian to have a real spectrum. In this paper we obtain the eigenvalues of a Dirac charged particle in a complex static and spherically symmetric potential.…

In this talk we review some recent results from random matrix models as applied to some non-perturbative issues in QCD. All of the issues we will discuss touched upon the important phenomenon related to the spontaneous breaking of chiral…

The action of the discrete symmetries on the scalar mode functions of the de Sitter spacetime is studied. The invariance with respect to a combination of discrete symmetries is put forward as a criterion to select a certain vacuum out of a…

The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…

We describe a general framework for avoiding spurious eigenvalues -- unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically…

We study perturbations of relative cubic Dirac operators for basic classical Lie superalgebras within the uniform formalism of the colour quantum Weil algebra. This perspective leads to three complementary classes of perturbations and…

We show that spin-flip probabilities emerge in the relativistic regime for scalar potentials, absent in the standard Dirac representation. We examine 1D scattering for the Dirac equation employing an alternate matrix representation…

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…

We present an approach to compute the electric and magnetic dipole moments of an electron by using polarization and magnetization parts of the Dirac current. We show that these dipole moment expressions obtained by our approach in this…

In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward we switch to an…

We show that the Dirac equation in 3+1 dimensions gives rise to supersymmetric patterns when the scalar and vector potentials are (i) Coulombic with arbitrary strengths or (ii) when their sum or difference is a constant, leading to…

In this article we investigate and solve exactly the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries through an algebraic approach. By focusing on the radial part of this problem, we use the Schr\"odinger…