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

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 نشر من قبل Loic Le Treust
 تاريخ النشر 2017
  مجال البحث فيزياء
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 تأليف Loic Le Treust




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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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