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.

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

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Naiara Arrizabalaga, Loïc Le Treust, Albert Mas, Nicolas Raymond. The MIT Bag Model as an infinite mass limit. 2018. ⟨hal-01863065v1⟩