Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors

Abstract

This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is self-adjoint on a usual Sobolev space whereas when the sector is non-convexit has a family of self-adjoint extensions parametrized by a complex number of theunit circle. As a byproduct of this analysis we are able to give self-adjointnessresults on polygones. We also discuss the question of distinguished self-adjointextensions and study basic spectral properties of the operator in the sector.

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• 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
• Spectral inequality for Dirac right triangles
• Dirac operator spectrum in tubes and layers with a zigzag type boundary
• Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors