Approximation of Dirac operators with \boldsymbolδ-shell potentials in the norm resolvent sense, II. Quantitative results

2025/07/02 by Jussi Behrndt, Behrndt, Jussi, Markus Holzmann +3
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2507.01482

Abstract

This paper is devoted to the approximation of two and three-dimensional Dirac operators H_\widetildeV δ_Σ with combinations of electrostatic and Lorentz scalar δ-shell interactions in the norm resolvent sense. Relying on results from \citeBHS23 an explicit smallness condition on the coupling parameters is derived so that H_\widetildeV δ_Σ is the limit of Dirac operators with scaled electrostatic and Lorentz scalar potentials. Via counterexamples it is shown that this condition is sharp. The approximation of H_\widetildeV δ_Σ for larger coupling constants is achieved by adding an additional scaled magnetic term.

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