Work

Dirac operators with Lorentz scalar shell interactions

Year: 2018

Type: article

Abstract: This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.

Source: Reviews in Mathematical Physics

DOI: 10.1142/s0129055x18500137

Authors: Markus Holzmann, Thomas Ourmières-Bonafos, Konstantin Pankrashkin

Institutions: Graz University of Technology, Université Paris-Sud, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: LabEx Mathématique Hadamard