On the virtual levels of positively projected massless Coulomb-Dirac   operators
  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. 
Sergey Morozov and David M\"uller
math-ph math.CA math.MP math.SP quant-ph