On the MIT bag model: self-adjointness and non-relativistic limit

Abstract

This paper is devoted to the mathematical investigation of the MIT bag model, that is the Dirac operator on a smooth and bounded domain with certain boundary conditions. We prove that the operator is self-adjoint and, when the mass goes to infinity, we provide spectral asymptotic results.

References in corpus (8)

• Little Magnetic Book
• The Calderon Projection: New Definition and Applications
• Spectral gaps of Dirac operators describing graphene quantum dots
• Boundary Value Problems for Elliptic Differential Operators of First Order
• Guide to Boundary Value Problems for Dirac-Type Operators
• An effective Hamiltonian for the eigenvalue asymptotics of a Robin Laplacian with a large parameter
• On the mathematical treatment of the Born-Oppenheimer approximation
• On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries

Cited by in corpus (17)

• Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors
• Dirac operators with Lorentz scalar shell interactions
• Self-adjoint Dirac operators on domains in ${\mathbb{R}}^3$
• Resolvent convergence to Dirac operators on planar domains
• Dirac operators on hypersurfaces as large mass limits
• A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities
• Spectral properties of relativistic quantum waveguides
• Spectral optimisation of Dirac rectangles
• Eigenvalue curves for generalized MIT bag models
• Boundary problems for three-dimensional Dirac operators and generalized MIT bag models for unbounded domains
• Spectral inequality for Dirac right triangles
• Dirac operator spectrum in tubes and layers with a zigzag type boundary
• Casimir energy for spinor fields with $\delta$-shell potentials
• Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• A Poincaré-Steklov map for the MIT bag model
• A generalized MIT Bag operator on spin manifolds in the non-relativistic limit