The MIT Bag Model as an infinite mass limit

Abstract

The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m>0$ lies outside a smooth and bounded open set $\Omega \subset {\mathbb{R}}^3$, 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.