A strategy for self-adjointness of Dirac operators: applications to the MIT bag model and \(\delta\)-shell interactions. (English) Zbl 06918953
Summary: We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a \(\mathcal{C}^2\)-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 \(\delta\)-shell interaction.
MSC:
47B25 | Linear symmetric and selfadjoint operators (unbounded) |
31B10 | Integral representations, integral operators, integral equations methods in higher dimensions |
35J67 | Boundary values of solutions to elliptic equations and elliptic systems |
35Q40 | PDEs in connection with quantum mechanics |
58J32 | Boundary value problems on manifolds |
81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |