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

Müller, David (2016): Minimax Principles, Hardy-Dirac Inequalities, and Operator Cores for Two and Three Dimensional Coulomb-Dirac Operators. In: Documenta Mathematica, Vol. 21: pp. 1151-1170

Abstract

For n is an element of{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(infinity)(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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1431-0643
• Language: English