The MIT Bag Model as an infinite mass limit
[Le modèle MIT bag obtenu comme une limite de masse grande]
Journal de l’École polytechnique — Mathématiques, Tome 6 (2019) , pp. 329-365.

Nous considérons l’opérateur de Dirac en dimension 3 dont la masse m>0 est supposée grande à l’extérieur d’un ouvert borné et régulier Ω 3 . Nous démontrons que son spectre approche celui de l’opérateur de Dirac sur Ω qui intègre dans son domaine les conditions au bord dites « MIT bag ». L’analyse asymptotique est réalisée grâce à l’usage de coordonnées tubulaires et à l’analyse d’un problème d’optimisation unidimensionnel dans la direction normale.

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 Ω 3 , it is proved that its spectrum approximates the one of the Dirac operator on Ω with the MIT bag boundary condition. The approximation, modulo an error of order o(1/m), is carried out by introducing tubular coordinates in a neighborhood of Ω and analyzing one dimensional optimization problems in the normal direction.

Reçu le : 2018-09-12
Accepté le : 2019-05-08
Publié le : 2019-05-23
DOI : https://doi.org/10.5802/jep.95
Classification : 35J60,  35Q75,  49J45,  49S05,  81Q10,  81V05,  35P15,  58C40
Mots clés: Opérateur de Dirac, particules relativistes dans une boîte, modèle MIT bag, théorie spectrale
@article{JEP_2019__6__329_0,
     author = {Naiara Arrizabalaga and Lo\"\i c Le Treust and Albert Mas and Nicolas Raymond},
     title = {The MIT Bag Model as an infinite mass limit},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {329--365},
     publisher = {\'Ecole polytechnique},
     volume = {6},
     year = {2019},
     doi = {10.5802/jep.95},
     zbl = {07070236},
     mrnumber = {3959076},
     language = {en},
     url = {jep.centre-mersenne.org/item/JEP_2019__6__329_0/}
}
Naiara Arrizabalaga; Loïc Le Treust; Albert Mas; Nicolas Raymond. The MIT Bag Model as an infinite mass limit. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019) , pp. 329-365. doi : 10.5802/jep.95. https://jep.centre-mersenne.org/item/JEP_2019__6__329_0/

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