A strategy for self-adjointness of Dirac operators: applications to the MIT bag model and δ-shell interactions

• Autores: Thomas Ourmières Bonafos, Luis Vega González
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 62, Nº 2, 2018, págs. 397-437
• Idioma: español
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• Resumen

  • We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a C 2 -compact surface without boundary. To do so we are lead to study the layer potential induced by the Dirac system as well as to define traces in a weak sense for functions in the appropriate Sobolev space. Finally, we introduce Calderón projectors associated with the problem and illustrate the method in two special cases: the well-known MIT bag model and an electrostatic δ-shell interaction.