Semiclassical Asymptotics of Eigenvalues for Dirac Operators with Magnetic Fields

The main purpose of the present paper is to investigate the semiclassical asymptotics of eigenvalues for the Dirac operator with magnetic fields. In the case of the Schr¨odinger operator with magnetic field, this problem was recently solved by Matsumoto. We show that the nth positive eigenvalue of the Dirac operator behaves like that of the associated Schr¨odinger operator via unitary equivalence of their spectral measures.