On the approximation of the Dirac operator coupled with confining Lorentz scalar δ-shell interactions

2024/04/11 by Mahdi Zreik, Zreik, Mahdi · 1 citation
Computer Science · Mathematics · #35P15 #58C40 #81Q10 #81V05 #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.07784

openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω₊⊂ℝ³ be a fixed bounded domain with boundary Σ= ∂Ω₊. We consider U^ε a tubular neighborhood of the surface Σ with a thickness parameter ε>0, and we define the perturbed Dirac operator \mathfrakD^ε_M=D_m +Mβ\mathbb1_U^ε, with D_m the free Dirac operator, M>0, and \mathbb1_{U ^ε} the characteristic function of U^ε. Then, in the norm resolvent sense, the Dirac operator \mathfrakD^ε_M converges to the Dirac operator coupled with Lorentz scalar δ-shell interactions as ε = M^-1 tends to 0, with a convergence rate of O(M^-1).

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