On the minimax principle for Coulomb-Dirac operators

2014/01/23 by S. V. Morozov, David Müller, Morozov, Sergey +1
Computer Science · Mathematics · #46N50 (Secondary) #49R05 (Primary) 81Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1401.5916

openalex publication_date 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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