Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors
Mathematical Physics
2019-04-25 v2 Analysis of PDEs
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1707.04000,
title = {Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors},
author = {Loïc Le Treust and Thomas Ourmières-Bonafos},
journal= {arXiv preprint arXiv:1707.04000},
year = {2019}
}