Minimax Principles, Hardy-Dirac Inequalities, and Operator Cores for Two and Three Dimensional Coulomb-Dirac Operators

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 socalled Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on C0 (R n \ {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. 2010 Mathematics Subject Classification: 49R05, 49J35, 81Q10