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

2016/03/04 by Müller, David
#49R05 81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1603.01557

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 C₀^∞(ℝⁿ∖\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.

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