ON THE SPECTRAL THEORY OF DIRAC OPERATORS WITH A VARIABLE MASS TERM

HUBERT KALF

Hubert.Kalf@mathematik.uni-muenchen.de

Mathematisches Institut

Universität München

Theresienstr. 39

D-80333 München, Germany

Universität München

Theresienstr. 39

D-80333 München, Germany

The spectrum of the Dirac operator is purely discrete when the mass
term ``dominates'' the potential (O. Yamada). In the opposite case one
expects the spectrum to be purely absolutely continuous. This was
proved when both the mass term and the potential are spherically
symmetric (K. M. Schmidt, O. Yamada). Using virial techniques, a
theorem is presented which establishes at least absence of eigenvalues
when mass term and potential are not necessarily rotationally
symmetric. This is joint work with T. Okaji (Kyoto) and O. Yamada
(Kusatsu).

Eastham Meeting at Gregynog, 26-27 July 2002