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

TL;DR

This paper analyzes the self-adjointness of two-dimensional Dirac operators with infinite mass boundary conditions in sectors, revealing how the sector's aperture influences self-adjointness and extending results to polygons.

Contribution

It provides a detailed study of self-adjointness depending on sector geometry and characterizes extensions, advancing understanding of Dirac operators in polygonal domains.

Findings

Self-adjointness depends on sector convexity.

Non-convex sectors admit a family of self-adjoint extensions.

Results extend to polygons and spectral properties are analyzed.

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.