Approximation of Dirac operators with δ‐shell potentials in the norm resolvent sense, II: Quantitative results

Mathematische Nachrichten 2026 Open access

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Authors: Jussi Behrndt, Markus Holzmann, Christian Stelzer‐Landauer
DOI: 10.1002/mana.70085
Cited by: 0
References: 32

Abstract

Abstract This paper is devoted to the approximation of two‐ and three‐dimensional Dirac operators with combinations of electrostatic and Lorentz scalar ‐shell interactions in the norm resolvent sense. Relying on results from Behrndt, Holzmann, and Stelzer‐Landauer [Math. Nachr. 298 (2025), 2499–2546], an explicit smallness condition on the coupling parameters is derived so that 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 for larger coupling constants is achieved by adding an additional scaled magnetic term.

Fields of Study & Subjects

Spectral Theory in Mathematical Physics Advanced Mathematical Physics Problems Mathematical and Theoretical Analysis

Publication details

Journal / source
Mathematische Nachrichten
Volume
299
Issue
4
Pages
704–763
Publication date
28 January 2026
Language
EN