Self-adjointness Of Dirac Operators Research Articles

Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors

This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is self-adjoint on a usual Sobolev space whereas when the sector is non-convexit has a family of self-adjoint extensions parametrized by a complex number of theunit circle. As a byproduct of this analysis we are able to give self-adjointnessresults on polygones. We also discuss the question of distinguished self-adjointextensions and study basic spectral properties of the operator in the sector.

Essential Self-Adjointness of Dirac Operators Under an Integral Consition on the Potential

We prove a criterion of Levitan–Otelbaev for the essential self-adjointness of Dirac operators. It involves an integral condition on the potential that in particular admits a Coulomb-type singularity with atomic number ≤ 118.

Remark on essential selfadjointness of Dirac operators with coulomb potentials

On considere des operateurs de Dirac A=∑ j=1 3 α j D j +P(x), P(x)=∑ j=1 N P j (x−a j ), D j =−i∂ j . On demontre que toutes les informations sur le caractere autoadjoint et l'invariance du spectre essentiel sont contenues dans l'inegalite ∥r −1 u∥≤Cμ∥α j D j +P)u∥

A remark on the essential self-adjointness of Dirac operators

On considere le caractere auto-adjoint essentiel des operateurs de Dirac definis sur [C 0 ∞ (R 3 )] 4 . On donne des conditions sur le potentiel

On the selfadjointness of Dirac operators with anomalous magnetic moment

We provide a new proof of Behncke's remarkable result that the Coulombic Dirac equation with nonzero anomalous magnetic moment is essentially selfadjoint (on Co( R3)4) for acny value of the Coulomb charge. In this note we shall consider Dirac operators. In the simplest version, these have the form (1) H=a*p+m/3#+ V where p = -iv on L2(R3) and H acts on L2(R3, d3x; C4). a, /3 are 4 x 4 matrices, written in terms of the conventional 2 x 2 Pauli sigma matrices, a, as 2 x 2 blocks of 2 x 2 matrices: A= I) a= (0) It is well known (see e.g. [1, 8, 9]) that for V = e Ix-.-, (1) is essentially selfadjoint on CO (R3)4 if and only if e 1 [11]. Indeed, it has been speculated that these difficulties have physical significance for the stability of the world if superheavy nucleii with charge Z > 137 exist (written back in conventional units Z = ea-' with a the fine structure constant); see [6, 10] and the references therein. We feel that these speculations are ill founded for a number of reasons including the theme of this note. Equation (1) corresponds to the equation for an electron with magnetic moment 1 (in units of Bohr magnetons), but it is known that the actual value is 1 + p where p = 0.001159 is called the anomalous magnetic moment [5] (understood from the point of view of quantum electrodynamics). Equation (1) in the presence of such an anomalous moment should be replaced by [13] (2) H=a-p-+m/3+ V2 MT V

On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators.

On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators.