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Journal Articles Journal de l'École polytechnique — Mathématiques Year : 2019

## The MIT Bag Model as an infinite mass limit

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Loïc Le Treust
Albert Mas
• Function : Author
• PersonId : 1035929
Nicolas Raymond
• Function : Author
• PersonId : 921144

#### 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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### Dates and versions

hal-01863065 , version 1 (28-08-2018)
hal-01863065 , version 2 (24-05-2019)

### Licence

Attribution - NonCommercial - ShareAlike - CC BY 4.0

### Identifiers

• HAL Id : hal-01863065 , version 2
• ARXIV :
• DOI :

### Cite

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

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