Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators
Abstract
We present new results on the block-diagonalization of Dirac operators on three-dimensional Euclidean space with unbounded potentials. Classes of admissible potentials include electromagnetic potentials with strong Coulomb singularities and more general matrix-valued potentials, even non-self-adjoint ones. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z=124 and prove the convergence of the Douglas-Kroll-He\ss\ approximation up to Z=62, thus improving the upper bounds Z=93 and Z=51, respectively, by H.\ Siedentop and E.\ Stockmeyer considerably. These results follow from abstract theorems on perturbations of spectral subspaces of operators with gaps, which are based on a method of H.\ Langer and C.\ Tretter and are also of independent interest.
Cite
@article{arxiv.1111.1361,
title = {Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators},
author = {Jean-Claude Cuenin},
journal= {arXiv preprint arXiv:1111.1361},
year = {2014}
}