  We consider transformation maps on the space of states which are symmetries
in the sense of Wigner. Due to the convex nature of the space of states, the
set of these maps has a convex structure. We investigate the possibility of a
complete characterization of extreme maps of this convex body, to be able to
contribute to the classification of positive maps. Our study provides a variant
of Wigner's theorem originally proved for ray transformations in Hilbert
spaces.
