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 enough and bounded open set Ω ⊂ R3, 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 introduc- ing tubular coordinates in a neighborhood of ∂Ω and analyzing one dimensional optimization problems in the normal direction.