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

This paper deals with the study of the two-dimensional Dirac operator with infinite mass boundary conditions in sectors. We investigate the question of self-adjointness depending on the aperture of the sector: when the sector is convex it is self-adjoint on a usual Sobolev space, whereas when the sector is non-convex it has a family of self-adjoint extensions parametrized by a complex number of the unit circle. As a by-product of the analysis, we are able to give self-adjointness results on polygonal domains. We also discuss the question of distinguished self-adjoint extensions and study basic spectral properties of the Dirac operator with a mass term in the sector.