Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators

Jean-Claude Cuenin

doi:10.1142/s0129055x12500213

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arXiv · 1111.1361

Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators

Jean-Claude Cuenin

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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.

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BibTeX RIS

Jean-Claude Cuenin. 2011-11-05. Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators. https://doi.org/10.1142/s0129055x12500213

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