The abstract theory of scattering

Asao Arai

First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rn is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.

Bernd Thaller

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.

Ajoy Kumar Ghatak, S. Lokanathan

Takashi Kato

Monotone dependence of the scattering phases and the total phase on the perturbing operator are proved on the basis of an explicit formula for the S-matrix in the framework of abstract scattering theory. The results are applied to scattering by potentials and by rigid obstacles.