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# The MIT Bag Model as an infinite mass limit

Abstract : The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m>0$ lies outside a smooth and bounded open set $\Omega\subset\R^3$, it is proved that its spectrum is approximated by the one of the Dirac operator on $\Omega$ with the MIT bag boundary condition. The approximation, which is developed up to and error of order $o(1/\sqrt m)$, is carried out by introducing tubular coordinates in a neighborhood of $\partial\Omega$ and analyzing the corresponding one dimensional optimization problems in the normal direction.
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Cited literature [19 references]

https://hal-amu.archives-ouvertes.fr/hal-01863065
Contributor : Loïc Le Treust Connect in order to contact the contributor
Submitted on : Friday, May 24, 2019 - 8:15:18 PM
Last modification on : Friday, May 20, 2022 - 9:04:50 AM

### File

ALMR19_8May.pdf
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### Citation

Naiara Arrizabalaga, Loïc Le Treust, Albert Mas, Nicolas Raymond. The MIT Bag Model as an infinite mass limit. Journal de l'École polytechnique — Mathématiques, École polytechnique, 2019, 6, pp.329-365. ⟨10.5802/jep.95⟩. ⟨hal-01863065v2⟩

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