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On the minimax principle for Coulomb-Dirac operators

Authors
  • Morozov, Sergey
  • Müller, David
Type
Preprint
Publication Date
Jan 23, 2014
Submission Date
Jan 23, 2014
Identifiers
arXiv ID: 1401.5916
Source
arXiv
License
Yellow
External links

Abstract

Let q and v be symmetric sesquilinear forms such that v is a form perturbation of q. Then we can associate a unique self-adjoint operator B to q+ v. Assuming that B has a gap (a, b) in the essential spectrum, we prove a minimax principle for the eigenvalues of B in (a, b) using a suitable orthogonal decomposition of the domain of q. This allows us to justify two minimax characterisations of eigenvalues in the gap of three-dimensional Dirac operators with electrostatic potentials having strong Coulomb singularities.

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