Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

Abstract

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