The MIT Bag Model as an infinite mass limit

Naiara Arrizabalaga (1) , Loïc Le Treust (2) , Albert Mas (3) , Nicolas Raymond (4, 5)

1 UPV/EHU - University of the Basque Country/Euskal Herriko Unibertsitatea
2 I2M - Institut de Mathématiques de Marseille
3 Departament de Matematiques i Informatica, Universitat de Barcelona
4 IRMAR - Institut de Recherche Mathématique de Rennes
5 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Keywords: relativistic particle in a box; spectral theory; MIT bag model; Dirac operator

Domains: Mathematics [math]; Analysis of PDEs [math.AP]; Mathematics [math]; Mathematical Physics [math-ph]; Mathematics [math]; Spectral Theory [math.SP]

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⟩