On the minimax principle for Coulomb-Dirac operators

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.

22 pages

References in corpus (1)

• On the eigenvalues of operators with gaps. Application to Dirac operators

Cited by in corpus (3)

• On the eigenvalues of operators with gaps. Application to Dirac operators
• Domains for Dirac-Coulomb min-max levels
• Dirac-Coulomb operators with general charge distribution. I. Distinguished extension and min-max formulas