Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

For a family of self-adjoint Dirac operators \(-i c (\alpha \cdot \nabla ) + \frac{c^2}{2}\) $-ic(\alpha ·\mathrm{\nabla })+\frac{c^2}{2}$ subject to generalized MIT bag boundary conditions on domains in \(\mathbb {R}^3\) ${\mathbb{R}}^3$ , 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.