Normal forms of an abstract Dirac operator and applications to scattering theory

Abstract

The unitary transformations which convert an abstract Dirac operator into an ‘‘even’’ (resp. ‘‘odd’’) operator are determined. The problem is formulated and solved completely within the general setup of supersymmetric quantum mechanics. This leads to some apparently new applications in relativistic quantum mechanics, where the transformations are known as the Foldy–Wouthuysen (resp. Cini–Touschek) transformations. The scattering theory for abstract Dirac operators is discussed and the utility of the general theory is illustrated by proving existence of relativistic Mo/ller operators for scattering from long-range magnetic fields.