

Here is a selection of my scientific achievements in the field of Mathematical Physics (numbers refer to the publication list). Much of this work is centered around the Dirac equation.
 Derivation of a formula for the first and secondorder relativistic corrections of eigenvalues of Schrödinger operators. First mathematically rigorous proof of the FoldyWouthuysen result (by analytic perturbation theory) about thirty years after its introduction [7], [9], [1].
 A supersymmetric proof that singularities produced by anomalous magnetic moments have in fact a regularizing influence in the Dirac equation [11].
 Established the asymptotic completeness of the Dirac equation with Coulomb potentials (using geometric methods and asymptotic observables). Asymptotic completeness is the basic mathematical requirement for the existence of a scattering theory [13].
 First proof of asymptotic completeness for the Schrödinger equation with longrange magnetic fields and for the Dirac equation with longrange potentials of a more general (nonelectrostatic) type. Discovery of the fact that a certain class of longrange magnetic fields are in fact shortrange in the Poincaré gauge [14], [15], [17].
 Proof of the first comparison theorem for Schrödinger operators with arbitrary magnetic fields in two dimensions (sort of diamagnetic inequality in the form of a heatkernel estimate) [20].
I have made contributions to the following research areas:
 essential selfadjointness
 scattering theory by stationary and timedependent methods
 asymptotic completeness for the Dirac eqation with longrange potentials
(also in the case of nonelectrostatic interactions, in particular magnetic fields)
 the nonrelativistic limit of the Dirac equation
 supersymmetry and normal forms of the Dirac equation
 heat kernel estimates for the Schrödinger equation with magnetic fields
 degenerate Cauchy problems


