On the approximation of the δ-shell interaction for the 3-D Dirac operator

2023/09/22 by Mahdi Zreik, Zreik, Mahdi · 1 citation
Mathematics · #35P15 #58C40 #81Q10 #81V05 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.12911

openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the three-dimensional Dirac operator coupled with a combination of electrostatic and Lorentz scalar δ-shell interactions. We approximate this operator with general local interactions V. Without any hypotheses of smallness on the potential V, converges in the strong resolvent sense to the Dirac Hamiltonian coupled with a δ-shell potential supported on §, a bounded smooth surface. However, the coupling constant depends nonlinearly on the potential V.

Cited by

• Approximation of Dirac operators with confining electrostatic and Lorentz scalar δ-shell potentials

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