On the virtual levels of positively projected massless Coulomb-Dirac operators

TL;DR

This paper investigates the spectral properties of various self-adjoint realizations of massless Coulomb-Dirac operators, identifying conditions for negative spectrum emergence under perturbations and providing explicit spectral representations.

Contribution

It introduces new conditions for negative spectrum emergence and derives weighted Lieb-Thirring estimates for these operators.

Findings

Negative spectrum appears under small negative perturbations in certain realizations.

Explicit spectral representations for all self-adjoint realizations on the half-line.

Weighted Lieb-Thirring estimates for negative eigenvalues.

Abstract

Considering different self-adjoint realisations of positively projected massless Coulomb-Dirac operators we find out, under which conditions any negative perturbation, however small, leads to emergence of negative spectrum. We also prove some weighted Lieb-Thirring estimates for negative eigenvalues of such operators. In the process we find explicit spectral representations for all self-adjoint realisations of massless Coulomb-Dirac operators on the half-line.