Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities.

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