Serge Richard, Rafael Tiedra de Aldecoa
On the spectrum of magnetic Dirac operators with Coulomb-type perturbations
(308K, Postscript)

ABSTRACT.  We carry out the spectral analysis of singular matrix valued 
perturbations of 3-dimensional Dirac operators with variable 
magnetic field of constant direction. Under suitable assumptions on 
the magnetic field and on the perturbations, we obtain a limiting 
absorption principle, we prove the absence of singular continuous 
spectrum in certain intervals and state properties of the point 
spectrum. Constant, periodic as well as diverging magnetic fields 
are covered, and Coulomb potentials up to the physical nuclear 
charge Z<137 are allowed. The importance of an internal-type 
operator (a 2-dimensional Dirac operator) is also revealed in our 
study. The proofs rely on commutator methods.