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

### David Müller

## Abstract

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 $C_{0}(R_{n}∖0;C_{2(n−1)})$, 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.

## Cite this article

David Müller, Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators. Doc. Math. 21 (2016), pp. 1151–1169

DOI 10.4171/DM/554