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

Thomas Ourmières-Bonafos and Luis Vega

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Abstract

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.

Article information

Source
Publ. Mat., Volume 62, Number 2 (2018), 397-437.

Dates
Received: 21 December 2016
Revised: 12 July 2017
First available in Project Euclid: 16 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.pm/1529114422

Digital Object Identifier
doi:10.5565/PUBLMAT6221804

Mathematical Reviews number (MathSciNet)
MR3815285

Zentralblatt MATH identifier
06918953

Subjects
Primary: 47B25: Symmetric and selfadjoint operators (unbounded)
Secondary: 31B10: Integral representations, integral operators, integral equations methods 35J67: Boundary values of solutions to elliptic equations 35Q40: PDEs in connection with quantum mechanics 58J32: Boundary value problems on manifolds 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords
Dirac operators self-adjoint extensions MIT bag model $\delta$-shell interactions

Citation

Ourmières-Bonafos, Thomas; Vega, Luis. A strategy for self-adjointness of Dirac operators: applications to the MIT bag model and $\delta$-shell interactions. Publ. Mat. 62 (2018), no. 2, 397--437. doi:10.5565/PUBLMAT6221804. https://projecteuclid.org/euclid.pm/1529114422


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