Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators

David Müller

Documenta mathematica, Tome 21 (2016), pp. 1151-1169

Résumé

For n∈2,3 we prove minimax characterisations of eigenvalues in the gap of the n dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value 1/(4−n). This result implies a so-called Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on C0∞​(Rn∖0;C2(n−1)), as long as the coupling constant does not exceed 1/(4−n). We also find an explicit description of an operator core of this operator.

Détail

DOI : 10.4171/dm/554

Classification : 49J35, 49R05, 81Q10
Mots-clés : minimax principle, Hardy-Dirac inequality, Coulomb-Dirac operator