Symmetry properties of the scattering path operator for arbitrary translationally invariant systems

In order to optimize the efficiency of relativistic band-structure calculations for complex systems, one should take full advantage of the magnetic space-group symmetry. Most important for the description of systems with reduced symmetry using the Korringa-Kohn-Rostoker method of band-structure calculation, a general derivation of magnetic symmetry properties of the scattering path operator both in real and reciprocal space is presented. In a straightforward way, this approach can be used to minimize the section of $\overrightarrow{k}$ space to be sampled for two- and three-dimensional numerical Brillouin-zone integration. Practical aspects of an implementation of the very general scheme presented are discussed in detail.