Eur. Phys. J. B 9, 577-582 (1999)
https://doi.org/10.1007/s100510050800

On the separability of relativistic electron propagators

Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Strasse 10, 48149 Münster, Germany

Corresponding author: ^a hzach@nwz.uni-muenster.de

Received: 1 July 1997
Published online: 15 June 1999

Abstract

In this contribution we examine the separability of relativistic electron propagators. Both, magnetic and non-magnetic systems are studied on the basis of the Kohn-Sham-Dirac equation. We find a Dirac-Green's function in excellent agreement with recent calculations utilizing the left and right-handed solutions to the Dirac equation. Starting from these Dirac-Green's functions we re-derive a rotation matrix formalism that was shown to result in separable scattering matrices in the non-relativistic case. It turns out, that spin-dependent scattering matrices can be formulated which are closely related to their non-relativistic counterparts. These matrices incorporate spin-flip and non spin-flip processes on an equal footing, but are irreducible to sums over composite rotation matrices. The latter result is a major drawback for numerical applications since electron scattering in terms of composite rotations had drawn a lot of attention recently.