Dirac operators on hypersurfaces as large mass limits

Abstract

We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in the whole space, with a suitably chosen zero order mass term.

arXiv comment39 pages

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Cited by in corpus (9)

• Two-dimensional Dirac operators with singular interactions supported on closed curves
• Self-adjoint Dirac operators on domains in ${\mathbb{R}}^3$
• A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities
• Eigenvalue curves for generalized MIT bag models
• Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions
• Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions
• Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$
• A generalized MIT Bag operator on spin manifolds in the non-relativistic limit
• A Poincaré-Steklov map for the MIT bag model