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

We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a C2 -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 Calder´on 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.