Dirac operators with Lorentz scalar shell interactions

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.

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Cited by in corpus (10)

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• Spectral Properties of the Dirac Operator coupled with $\delta$-Shell Interactions
• Dirac operators on hypersurfaces as large mass limits
• Spectral Analysis of Dirac Operators with delta interactions supported on the boundaries of rough domains
• A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Eigenvalue curves for generalized MIT bag models
• Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors