Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

For a family of self-adjoint Dirac operators -i c (α · ∇ ) + c²/2 - i c ( α · ∇ ) + c 2 2 subject to generalized MIT bag boundary conditions on domains in R³ 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 .