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

Mahdi Zreik

doi:10.56754/0719-0646.2603.489

DOI:

https://doi.org/10.56754/0719-0646.2603.489

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 \(V\), we investigate convergence in the strong resolvent sense to the Dirac Hamiltonian coupled with a δ-shell potential supported on \(S\), a bounded smooth surface. However, the coupling constant depends nonlinearly on the potential \(V\).

Keywords

Dirac operators , self-adjoint operators , shell interactions , non critical and non-confining interaction strengths , approximations

Mathematics Subject Classification:

81Q10 , 81V05 , 35P15 , 58C40

Mahdi Zreik Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux 33405 Talence Cedex, France – Departamento de Matemáticas, Universidad del País Vasco, Barrio Sarriena s/n 48940 Leioa, Spain, and Basque Center for Applied Mathematics (BCAM), Spain. https://orcid.org/0000-0002-9891-0525

Pages: 489–505
Date Published: 2024-12-11
Vol. 26 No. 3 (2024)

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