A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and $\delta$-shell interactions

Abstract

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 Calderon 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.