A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and $\delta$-shell interactions
Copyright policy )A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and $\delta$-shell interactions
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 Calder��n projectors associated with the problem and illustrate the method in two special cases: the well-known MIT bag model and an electrostatic $��$-shell interaction.
$\delta$-shell interactions, Dirac operators, FOS: Physical sciences, Mathematical Physics (math-ph), 31B10, 58J32, 47B25, 31B10, 35J67, 35Q40, 58J32, 81Q10, Mathematics - Analysis of PDEs, 35Q40, 81Q10, self-adjoint extensions, 35J67, FOS: Mathematics, 47B25, MIT bag model, Mathematical Physics, Analysis of PDEs (math.AP)
$\delta$-shell interactions, Dirac operators, FOS: Physical sciences, Mathematical Physics (math-ph), 31B10, 58J32, 47B25, 31B10, 35J67, 35Q40, 58J32, 81Q10, Mathematics - Analysis of PDEs, 35Q40, 81Q10, self-adjoint extensions, 35J67, FOS: Mathematics, 47B25, MIT bag model, Mathematical Physics, Analysis of PDEs (math.AP)
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