The MIT Bag Model as an infinite mass limit
Naiara Arrizabalaga; Loïc Le Treust; Albert Mas; Nicolas Raymond
Journal de l'École polytechnique — Mathématiques, Volume 6 (2019), p. 327-363

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.

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.

Received : 2018-09-12
Accepted : 2019-05-08
Published online : 2019-06-12
DOI : https://doi.org/10.5802/jep.95
Classification:  35J60,  35Q75,  49J45,  49S05,  81Q10,  81V05,  35P15,  58C40
Keywords: Dirac operator, relativistic particle in a box, MIT bag model, spectral theory
@article{JEP_2019__6__327_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},
     publisher = {\'Ecole polytechnique},
     volume = {6},
     year = {2019},
     pages = {327-363},
     doi = {10.5802/jep.95},
     language = {en},
     url = {https://jep.centre-mersenne.org/item/JEP_2019__6__327_0}
}
The MIT Bag Model as an infinite mass limit. Journal de l'École polytechnique — Mathématiques, Volume 6 (2019) pp. 327-363. doi : 10.5802/jep.95. https://jep.centre-mersenne.org/item/JEP_2019__6__327_0/

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