The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass lies outside a smooth enough and bounded open set , it is proved that its spectrum approximates the one of the Dirac operator on with the MIT bag boundary condition. The approximation, modulo an error of order , is carried out by introducing tubular coordinates in a neighborhood of and analyzing one dimensional optimization problems in the normal direction.
Nous considérons l’opérateur de Dirac en dimension dont la masse est supposée grande à l’extérieur d’un ouvert borné et régulier . Nous démontrons que son spectre approche celui de l’opérateur de Dirac sur 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.
Accepted:
Published online:
DOI: 10.5802/jep.95
Keywords: Dirac operator, relativistic particle in a box, MIT bag model, spectral theory
Mot clés : Opérateur de Dirac, particules relativistes dans une boîte, modèle MIT bag, théorie spectrale
Naiara Arrizabalaga 1; Loïc Le Treust 2; Albert Mas 3; Nicolas Raymond 4
@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{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {329--365}, publisher = {\'Ecole polytechnique}, volume = {6}, year = {2019}, doi = {10.5802/jep.95}, mrnumber = {3959076}, zbl = {07070236}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.95/} }
TY - JOUR AU - Naiara Arrizabalaga AU - Loïc Le Treust AU - Albert Mas AU - Nicolas Raymond TI - The MIT Bag Model as an infinite mass limit JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 329 EP - 365 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.95/ DO - 10.5802/jep.95 LA - en ID - JEP_2019__6__329_0 ER -
%0 Journal Article %A Naiara Arrizabalaga %A Loïc Le Treust %A Albert Mas %A Nicolas Raymond %T The MIT Bag Model as an infinite mass limit %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 329-365 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.95/ %R 10.5802/jep.95 %G en %F 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, Volume 6 (2019), pp. 329-365. doi : 10.5802/jep.95. https://jep.centre-mersenne.org/articles/10.5802/jep.95/
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