Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

For a family of self-adjoint Dirac operators $-ic(\alpha \cdot \mathrm{\nabla })+\frac{c^2}{2}$ subject to generalized MIT bag boundary conditions on domains in ${\mathbb{R}}^3$ it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large $c$.