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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
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