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

  • David Müller

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

For n2,3n\in{2,3} we prove minimax characterisations of eigenvalues in the gap of the nn dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value 1/(4n)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(Rn0;C2(n1))C_{0}^{\infty}({R}^{n}\setminus{0};{C}^{2(n-1)}), as long as the coupling constant does not exceed 1/(4n)1/(4-n). We also find an explicit description of an operator core of this operator.

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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