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The MIT bag model as an infinite mass limit. (Le modèle MIT bag obtenu comme une limite de masse grande.) (English. French summary) Zbl 1420.35094
Summary: The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass \(m>0\) lies outside a smooth enough and bounded open set \(\Omega \subset \mathbb{R}^3\), it is proved that its spectrum approximates the one of the Dirac operator on \(\Omega \) with the MIT bag boundary condition. The approximation, modulo an error of order \(o(1/\sqrt{m})\), is carried out by introducing tubular coordinates in a neighborhood of \(\partial \Omega \) and analyzing one dimensional optimization problems in the normal direction.

MSC:
35J60 Nonlinear elliptic equations
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35P15 Estimates of eigenvalues in context of PDEs
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