A strategy for self-adjointness of Dirac operators

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 appr...

Full description

Bibliographic Details
Authors: Ourmières-Bonafos, Thomas, Vega, Luis
Format: article
Publication Date:2018
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:191238
Online Access:https://ddd.uab.cat/record/191238
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6221804
Access Level:Open access
Keyword:Dirac operators
Self-adjoint extensions
Mit bag model
δ-shell interactions
Description
Summary: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.